The plane must fly at an angle of 11.31 degrees west of due north to arrive at the destination in the shortest time possible.
To determine the direction that the plane must fly relative to north, we need to first determine the actual velocity of the plane relative to the ground.
Let's break down the velocity vectors involved in the flight:
The air speed of the plane is 120 m/s in a direction perpendicular to the plane's heading (i.e., to the east).
The wind speed is 24 m/s due west.
Using vector addition, we can find the resultant velocity vector of the plane relative to the ground:
The eastward component of the plane's velocity is 120 m/s.
The westward component of the wind's velocity is 24 m/s.
The northward component of the plane's velocity is unknown and will depend on the plane's heading.
We can use the Pythagorean theorem to find the magnitude of the resultant velocity vector:
[tex]resultant speed^2 = eastward speed^2 + northward speed^2[/tex]
[tex]resultant speed^2 = (120 m/s)^2 + northward speed^2[/tex]
resultant speed = [tex]\sqrt{[(120 m/s)^2 + northward speed^2]}[/tex]
Since the destination is directly north of the origin, the plane's heading must be northward. Therefore, the angle between the plane's velocity vector and the northward direction must be the direction we're looking for.
To find this angle, we can use trigonometry. Let theta be the angle between the plane's velocity vector and the northward direction. Then:
tan(theta) = northward speed / 120 m/s
northward speed = 120 m/s * tan(theta)
Substituting this into the equation for the magnitude of the resultant velocity vector, we get:
resultant speed = [tex]\sqrt{[(120 m/s)^2 + (120 m/s * tan(theta))^2]}[/tex]
We want the resultant velocity vector to be equal to the distance between the two points on the ground (500 km) divided by the time of the flight. We can convert this to meters per second by dividing by the duration of the flight in seconds:
resultant speed = 500000 m / (flight time in seconds)
Equating this with the expression we derived for the magnitude of the resultant velocity vector, we get:
500000 m / (flight time in seconds) = [tex]\sqrt{[(120 m/s)^2 + (120 m/s * tan(theta))^2]}[/tex]
Solving for the flight time in seconds and simplifying, we get:
flight time = [tex]500000 m \sqrt{[(120 m/s)^2 + (120 m/s * tan(theta))^2]}[/tex]
To minimize the flight time, we need to maximize the northward component of the plane's velocity. We can do this by making the angle theta as small as possible, i.e., by flying as close to due north as possible.
Taking the derivative of the flight time expression with respect to theta, we get:
d(flight time) / d(theta) =[tex]-60000 * tan(theta) / (120^2 * (1 + tan(theta)^2)^(3/2))[/tex]
Setting this equal to zero, we find that the optimal value of theta is arctan(1/5), which is approximately 11.31 degrees. Therefore, the plane must fly at an angle of 11.31 degrees west of due north to arrive at the destination in the shortest time possible.
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Which of the following light waves can NOT penetrate the atmosphere and reach the ground?
A. Infrared wave.
B. Visible light.
C. Ultraviolet wave.
D. Radio wave.
Answer:
C) is apparently the answer required
Infrared tans, and you know that visible light and radio waves reach the ground
Ultraviolet is considered to be light shorter than 400 millimicrons
Some ultraviolet passes thru the atmosphere - (maybe 300-400 mυ)
Ordinary window glass absorbs light shorter than about 380 mυ
Some UV light is transmitted by the atmosphere
Normally, UV is divided into UV-A, UV-B, and UV-C and UV-A is transmitted by the atmosphere
If the cushion hits the ground at 12m/s , what is the minimum distance that it must compress on impact to ensure that the egg is unscathed? note: the acceleration associated with stopping the egg is so great that you can neglect gravity while the cushion is slowing due to contact with the ground.
Therefore, the cushion must compress at least 0.74 millimeters to ensure that the egg is unscathed.
What is acceleration?Acceleration is the rate of change of velocity over time. It is a vector quantity, which means it has both magnitude and direction. It can be expressed mathematically as the change in velocity divided by the change in time, or a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time. Acceleration is measured in units of meters per second squared (m/s²) in the International System of Units (SI).
Here,
Assuming that the cushion provides a constant deceleration to stop the egg and that the time of contact between the cushion and the ground is negligible, we can use the formula for deceleration:
v² = u² - 2as
where v is the final velocity (0 m/s), u is the initial velocity (12 m/s), a is the deceleration, and s is the distance the cushion compresses.
Solving for s, we get:
s = (u² - v²) / 2a
Since the acceleration is the deceleration and is negative, we can rewrite the formula as:
s = (u² - v²) / 2(-a)
Substituting the given values, we get:
s = (12² - 0²) / 2(-a)
We don't know the value of a, but we do know that the egg must be unscathed, which means that the acceleration must be small enough to prevent it from breaking. Let's assume a maximum safe acceleration of 100 g (where g is the acceleration due to gravity), which is a common standard for crash testing.
100 g = 100 * 9.8 m/s² = 980 m/s²
So we want to find the smallest distance s that satisfies:
a >= -980 m/s²
s = (12² - 0²) / 2(-980) = 0.00074 meters, or about 0.74 millimeters.
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Vector E is 0.111m long in a 90 degree direction. Vector F if 0.234m long in 300 degree direction. Find the magnitude of their vector sum
The magnitude of their vector sum is 0.149 m.
What is magnitude?
Magnitude is a measure of the size or intensity of a physical quantity. It can refer to the size of an earthquake, the brightness of a star, the intensity of a hurricane, or any other physical quantity that can be measured in size or intensity.
Ex = Ecose (0.111) cos90° = 0 =
Ey Esino (0.111)sin90° 0.111m =
And
Fr=Fcose (0.234) cos300° 0.117m = Fy = Fsin0 (0.234) sin300°-0.203m
So the components of the vector sum are
Rr Ex+Fr=0+0.1170.117m =
Ry = EyFy 0.111 -0.203-0.092m
The magnitude of the vector sum is
R= |R² + R² = √(0.117)2 + (−0.092)2 = 0.149m
Therefore, The magnitude of their vector sum is 0.149 m.
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the position of a pinewood derby car was observed at various times; the results are summarized in the following table. find the average velocity of the car for the following time periods.
The position of a pinewood derby car was observed at various times; the results are summarized in the following table therefore the average velocity of the car for the following time periods is 11.04m/s.
What is Velocity?
This is referred to as the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time.
Velocity = distance/time
This therefore means that velocity = v5 - v1 / t5- t1
Velocity = 57.5 - 2.3 / 5- 0
= 55.2/5 = 11.04m/s
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The full question is:
the position of a pinewood derby car was observed at various times; the results are summarized in the following table. find the average velocity of the car for the following time periods.
T(s) 0 1 2 3 4 5
X(m)0 2.3 9.2 20.7 36.8 57.5
when a sprinter uses starting blocks to enhance running performance, which of newton's laws is best represented by the interaction of the sprinter and the blocksa. First
b. Third
c. Law of universal gravitation
d. Second
The sprinter uses starting blocks to enhance running. When the sprinter pushes on the block the block push in turn with the same force and helps the runner to move forward. Hence, they are using Newton's third law of motion.
What is Newton's third law of motion ?Newton proposed three laws of motion. The first law describes the inertia of an object to stay in its current state until an external force acts on it. Second law of motion states that, the force exerted on an object is the product of its mass and acceleration.
Newton's third law of motion states that , for every action, there is an equal and opposite reaction. The sprinters uses the starting blocks to start running where, they push against the block results in a push with an equal force from the block.
This opposite force from the block helps to make the runner run fastly. Hence, Newton's third law is used here.
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show that the liquid-level system consisting of two interacting tanks (fig. 6.11) exhibits overdamped dynamics; that is, show that the damping coefficient in eq. 6-57 is larger than one.
The liquid-level system consisting of two interacting tanks exhibits overdamped dynamics when the damping coefficient in equation 6-57 is larger than one. This means that the system will return to equilibrium without oscillating.
To show that the damping coefficient is larger than one, we can use the equation 6-57:
H1' (s) / Q'i (s) = K'_1 (T_{ \alpha} s + 1) / \tau^2 s^2 + 2 \zeta \tau s + 1
where ζ is the damping coefficient, ωn is the natural frequency of the system, y is the displacement of the liquid level from equilibrium, and t is time.
The damping coefficient ζ is given by:
ζ = (R1 + R2)/2√(L1C1L2C2)
where R1 and R2 are the resistances of the two tanks, L1 and L2 are the inductances of the two tanks, and C1 and C2 are the capacitances of the two tanks.
If the damping coefficient ζ is larger than one, the system will exhibit overdamped dynamics. This means that the system will return to equilibrium without oscillating.
To show that the damping coefficient is larger than one, we can plug in the values of R1, R2, L1, L2, C1, and C2 into the equation for ζ and see if the result is larger than one.
If the result is larger than one, then the system exhibits overdamped dynamics. If the result is less than one, then the system exhibits underdamped dynamics. If the result is equal to one, then the system exhibits critically damped dynamics.
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Find the velocities of iron blocks weighing 50 kg and 100 kg if they are dropped from a height of 100 m at the same time.
Answer:
44.294 m/s
you might want to double check the answer depending on what you use for g. some people use 9.81, some 9.8, and some 10. that can effect the final answer
Explanation:
use the formula [tex]v^{2}-v_{0}^{2} = 2ax[/tex], which can be moved around to get [tex]v = \sqrt{2ax}[/tex]
note that mass does not effect the velocity
since the blocks were dropped from rest, v_0 = 0m/s. a = g = 9.81 m/s^2, and x = h = 100m.
plug in the values for the variables to get v = sqrt(2(9.81)(100)) = 44.294 m/s for both blocks
ou are conducting an experiment inside an elevator that can move in a vertical shaft. a load is hung vertically from the ceiling on a string, and is stationary with respect to you. the tension in the string is measured to be 10% less than the force due to gravity on the load. no other forces are acting on the load. which of the following statements about the elevator are correct?check all that apply.you are conducting an experiment inside an elevator that can move in a vertical shaft. a load is hung vertically from the ceiling on a string, and is stationary with respect to you. the tension in the string is measured to be 10% less than the force due to gravity on the load. no other forces are acting on the load. which of the following statements about the elevator are correct?check all that apply.the elevator is an inertial frame of reference.the elevator is not an inertial frame of reference.the elevator may be at rest for the duration of the entire experiment.the elevator may be moving at a constant velocity upward.the elevator may be moving at a constant velocity downward.the elevator must be accelerating. physics is beautifull
A frame of reference that is inertial is not the elevator.
The elevator must be accelerating.
What is Acceleration?
It is a vector quantity, which means that it has both magnitude and direction. Acceleration is defined as the change in velocity divided by the time it takes for that change to occur. Mathematically, acceleration can be expressed as:
a = (v_f - v_i) / t
where "a" is acceleration, "v_f" is the final velocity, "v_i" is the initial velocity, and "t" is the time taken for the change in velocity.
According to the problem statement, the tension in the string is measured to be 10% less than the force due to gravity on the load. This means that the net force on the load is not zero, and it is accelerating in the direction of the net force, which is downwards.
Since the load is stationary with respect to the observer inside the elevator, the elevator must also be accelerating downwards with an acceleration equal to that of the load. This implies that the elevator is not an inertial frame of reference, as an inertial frame of reference is a frame in which an object at rest remains at rest, or an object in motion moves with a constant velocity in a straight line, in the absence of any external forces.
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Assuming that autografts and isografts are not possible what is the next most successful graft type and what is the source
The next most successful graft type and what is the source of killer t cells and macrophages energy. if Assuming that autografts and isografts are not possible.
What is the source of macrophage?CCR2− macrophages are largely derived from embryonic progenitors, including contributions from yolk sac macrophages, and are primarily autonomous from blood monocytes. energy, in physics, is the capacity to do work. In contrast, resident cardiac CCR2+ macrophages are derived entirely from definitive HSCs and are replaced slowly by blood monocytes.
Are macrophages in urine?energy is the ability to do work. T cells and macrophages appear in the urine of patients with glomerulonephritis (GN), accompanied by active cellular infiltration such as cellular crescent formation and diffuse interstitial cell infiltration, but not in the urine of patients with GN without the active inflammatory lesions.
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a turntable is rotating at 3313rpm . you then flip a switch, and the turntable speeds up, with constant angular acceleration, until it reaches 78rpm . part g suppose you are asked to find the amount of time t , in seconds, it takes for the turntable to reach its final rotational speed. which of the following equations could you use to directly solve for the numerical value of t ?
Once t can be located, more details are required.You would need further information (namely, the amount of the rotational motion ) before you could discover a numerical value for t; knowing and 0 would not be sufficient to enable you to solve for t.
What does rotation about just a fixed axis entail?When every particle in a body revolves in a circle around a single line, this is known as pure rotational motion.The rotational axis is this line.Then, at the same time, the same deflection occurs in all of the radii vectors from of the shaft to all of the particles.
What quantity is regarded when the rotation's axis is fixed—angular velocity?A spinning object's angular velocity is defined as a vector quantity in more sophisticated investigations of rotational motion.This vector has magnitude and points exteriorly along the axis of rotation for an object revolving anticlockwise about a fixed axis.
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A ball falls from a shelf. Assuming there is no friction, why is the conservation of mechanical energy independent of mass?.
The conservation of mechanical energy is independent of mass because the energy is proportional to both mass and velocity, and any changes in one factor are balanced out by changes in the other factor.
The conservation of mechanical energy is a fundamental principle in physics that states that the total amount of mechanical energy in a closed system remains constant over time, provided that no external forces act on the system.
When a ball falls from a shelf, its potential energy (due to its position above the ground) is converted into kinetic energy (due to its motion as it falls). The total amount of mechanical energy in the system (the ball and the Earth) is conserved, even though the mass of the ball is different from the mass of Earth.
This is because the potential energy of the ball is proportional to its mass and height above the ground, while the kinetic energy of the ball is proportional to its mass and velocity. As the ball falls, its potential energy decreases, while its kinetic energy increases by an equal amount, such that the total mechanical energy of the system (ball and Earth) remains constant.
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Answer: Mass is eliminated when equating gravitational potential energy with kinetic energy.
Explanation:
A pickup truck, parked on a hill that is 11.8 m high, is accidently left in neutral without the parking brake applied.
The truck begins rolling down the hill. At the bottom, it continues rolling along a horizontal road. A 104.3-kg man jumps in the back, causing the truck's speed to reduce to 14.5 m/s. What is the mass of the truck? Ignore friction
The mass of the truck is equal to (104.3 kg x 14.5 m/s) / 11.8 m/s, which is approximately 119.4 kg.
What is mass?Mass is a measure of the amount of matter contained in an object. It can be measured using scales, balances or other measuring instruments. Mass is a fundamental property of all matter, and its measurement is the basis for many scientific and engineering calculations. Mass is not the same as weight, which is a measure of the force exerted by gravity on an object. Mass is often expressed in units such as kilograms or grams.
The mass of the truck can be determined using the law of conservation of momentum. Momentum is defined as the product of mass and velocity, so the momentum of the truck before the man jumps in is equal to the momentum of the truck and man after the man jumps in.
The momentum of the truck before the man jumps in is equal to the truck's mass multiplied by its velocity, which is 11.8 m/s. The momentum of the truck and man after the man jumps in is equal to the mass of the truck plus the man, multiplied by the reduced velocity of 14.5 m/s.
Therefore, the mass of the truck is equal to (104.3 kg x 14.5 m/s) / 11.8 m/s, which is approximately 119.4 kg.
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The sketch below shows cross sections of equipotential surfaces between two charged conductors that are shown in solid grey. Various points on the equipotential surfaces near the conductors are labeled A, B, C, ..., I.
At which of the labeled points will the electric field have the greatest magnitude?
A) G
B) I
C) A
D) H
E) D
The answer is B) I. The electric field will have the greatest magnitude at point I because it is the closest point to the charged conductors. The closer to the conductors, the greater the electric field magnitude.
What is electric field?Electric field is an invisible force field that surrounds any object that has an electric charge. It is measured in terms of volts per meter (V/m) and is responsible for the attraction or repulsion of two objects with different electric charges. The force of the electric field is determined by the amount of charge on the objects and the distance between them. Any changes in the electric field will cause a corresponding change in the force felt by the objects. Electric fields can be created by moving charges, such as those found in electric currents, or by static charges, such as those found on a charged object. Electric fields are essential for the transmission of electrical signals and are used in many applications, from telecommunications to medical imaging.
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A positive test charge is brought near to, but not touching a conducting sphere that is connected to the ground. Both objects remain at rest in the positions shown above. Charge begins to flow from the ground to the sphere. Which of the following statements best describes when charge stops flowing and provides justification for the claim? Charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of the test charge, because then the excess charge on the surface of the sphere will be equal to the charge of the test charge Charge will flow until the electric field at the surface of the sphere is equivalent to the electric field of the test charge, because then the net force on all charges on the surface of the sphere will be zero Charge will flow until the potential at the surface of the sphere is the same as the potential of the test charge, because then the net force on all charges on the surface of the sphere will be zero. Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the excess charge on the surface of the sphere will be equal to the charge of the test charge. Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the net force on all charges on the surface of the sphere will be zero
The correct statement is option - {D} : Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the net force on all charges on the surface of the sphere will be zero
What is a conducting sphere?A conducting sphere will have the complete charge on its outside surface and the electric field intensity inside the conducting sphere will be zero.For a spherical charged shell the entire charge will reside on outer surface and again there will be no field anywhere inside itGiven is a positive test charge is brought near to, but not touching a conducting sphere that is connected to the ground. Both objects remain at rest in the positions shown above. Charge begins to flow from the ground to the sphere
When charge stops flowing, charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the net force on all charges on the surface of the sphere will be zeroTherefore, the correct statement is option - {D} : Charge will flow from the ground to the sphere until the potential is the same everywhere within the sphere, because then the net force on all charges on the surface of the sphere will be zero
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Wind currents move from high to low pressure. true or flase
Answer:
TRUE
Explanation:
Gases move from high-pressure area to low-pressure area
in an electroscope being charged by induction, what happens when the charging rod is moved away before the ground is removed from the knob?
The electroscope will remain charged and continue to show the presence of an electric charge if the ground is withdrawn from the knob before the charging rod is removed.
An early scientific tool used to find electrical charge on a body is called an electroscope. The movement of a test object caused by the Coulomb electrostatic force is used to detect charge. Voltage and charge on an object are inversely correlated.
There are three traditional electroscope types: the needle electroscope, the gold-leaf electroscope, and the pith-ball electroscope (third).
electroscopes are utilized to determine whether a body has an electric charge. The movement of a test object caused by the Coulomb electrostatic force is used to detect charge. Voltage and charge on an object are inversely correlated.
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What force is required to accelerate a 3kg object at 12m/s²?
Answer:
Force = 36N
Explanation:
Force = Mass x Acceleration
Force = 3kg x 12m/s²
Force = 36N
60. A friction block consists of a piece of wood with slotted masses on top of it. If you double the total mass of the block plus slotted masses, how does the coefficient of static friction between the friction block and concrete change?
The change in the coefficient of static friction between the friction block and concrete change would be Zero which means it will not change.
How does mass affect the coefficient of static friction?The coefficient of static friction between two surfaces does not depend on the mass of the object. Therefore, doubling the total mass of the friction block and slotted masses would not change the coefficient of static friction between the block and the concrete.
The coefficient of static friction is a property of the two surfaces in contact and is affected by factors such as the roughness of the surfaces, the materials they are made of, and the amount of force pressing the surfaces together.
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Hair Growth
WARNING: This homework problem is out of left field. It has nothing to do with anything covered in the class. It is just a fun problem to practice unit conversions. It really annoys some people, but it has become a tradition so I'm leaving it in. Buckle up. The subsequent problems will all be on topic.
1a) Suppose your hair grows at the rate of 1/35 in per day. Find the rate at which your hair grows in nm/s.
1b) If an atomic layer is approximately 0.1nm thick, how fast are the protein synthesis machines working in atomic layer/s?
(a) The rate at which your hair grows is approximately 20.3 nm/s.
(b) The protein synthesis machines are working at a rate of approximately 203.2 atomic layers/s.
What is the rate at which your hair grows in nm/s?
First, we need to convert the rate of hair growth from inches per day to nanometers per second. There are 2.54 centimeters in an inch, and 10 million nanometers in a centimeter.
So, we can calculate:
1/35 inch per day = (1/35) x 2.54 cm/inch x 10^7 nm/cm x 1 day/86400 s
= 20.319 nm/s (rounded to three significant figures)
If an atomic layer is approximately 0.1nm thick, then the number of atomic layers formed in one second will be the ratio of the growth rate of the protein synthesis machines to the thickness of an atomic layer.
We can use the growth rate we calculated in part (a) and divide it by 0.1 nm to find the number of atomic layers formed per second:
20.319 nm/s / 0.1 nm/layer = 203.19 layers/s
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1. A charge of 6.4 C passes through a cross-sectional area or conductor in 2s. How much charge will pass through a cross sectional area of the conductor in 1 min?
The amount of charge that will pass through the cross-sectional area of the conductor in 1 min is 192 C.
What is the amount of charge?
We can use the formula Q = I * t,
where;
Q is the amount of charge, I is the current, and t is the time.Given that a charge of 6.4 C passes through a cross-sectional area of the conductor in 2 s, we can find the current using the formula:
I = Q / t = 6.4 C / 2 s = 3.2 A
So, the current through the conductor is 3.2 A.
To find the amount of charge that will pass through the cross-sectional area of the conductor in 1 min (60 s), we can use the same formula:
Q = I * t = 3.2 A * 60 s = 192 C
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URGENT HELP:
Two sine waves of equal frequency are to be compounded, (1) a1= 3.0 × 10–6 m and ϕ0 = 60° and (2) a2= 4.0 × 10–6 m and ϕ0 = 150°. (a) Calculate their resultant amplitude, (b) What is the resultant’s initial phase angle. (c) Draw a circle of reference and a time graph for the sine waves.
Answer:
Explanation:
To solve this problem, we can use the following equations for the addition of two sinusoidal waves:
y1 = A1 sin(ωt + φ1)
y2 = A2 sin(ωt + φ2)
where A1 and A2 are the amplitudes of the waves, ω is the angular frequency, t is time, and φ1 and φ2 are the initial phase angles.
(a) To find the resultant amplitude of the two waves, we can use the following equation:
Ar = √(A1^2 + A2^2 + 2A1A2cos(φ2 - φ1))
where Ar is the resultant amplitude.
Substituting the given values, we get:
Ar = √((3.0 × 10^(-6))^2 + (4.0 × 10^(-6))^2 + 2(3.0 × 10^(-6))(4.0 × 10^(-6))cos(150° - 60°))
Ar ≈ 5.03 × 10^(-6) m
Therefore, the resultant amplitude is approximately 5.03 × 10^(-6) m.
(b) To find the resultant's initial phase angle, we can use the following equation:
tan(φr) = (A1sin(φ1) + A2sin(φ2))/(A1cos(φ1) + A2cos(φ2))
where φr is the initial phase angle of the resultant wave.
Substituting the given values, we get:
tan(φr) = (3.0 × 10^(-6)sin(60°) + 4.0 × 10^(-6)sin(150°))/(3.0 × 10^(-6)cos(60°) + 4.0 × 10^(-6)cos(150°))
φr ≈ 142.85°
Therefore, the resultant's initial phase angle is approximately 142.85°.
(c) The circle of reference and the time graph for the sine waves can be drawn as follows:
Sine Waves
The blue and red arrows represent the maximum displacement of the waves. The black arrow represents the displacement of the resultant wave. The time graph shows the displacement of each wave and the resultant wave over time.
Because weight is a measurement of the amount of gravity pulling on an object, weight is considered a ______.
Answer:
Weight is considered a force, since it is a measurement of the amount of gravity pulling on an object.
Calculate the force of gravity on the 0.70- kg mass if it were 1.9×10^7 m above Earth's surface (that is, if it were four Earth radii from Earth's center).
Answer:
This answer his answers is quite long but here's your answer
Explanation:
The force of gravity on an object depends on two factors: the mass of the object and the distance between the object and the center of the Earth. The formula to calculate the force of gravity is:
F = G * (m1 * m2) / r^2
where F is the force of gravity, G is the gravitational constant (6.67 x 10^-11 N m^2/kg^2), m1 is the mass of the first object (in this case, the mass of the Earth), m2 is the mass of the second object (0.70 kg), and r is the distance between the centers of the two objects (in this case, the distance between the center of the Earth and the 0.70 kg mass, which is 4 times the radius of the Earth, or 4 * 6,371 km = 25,484 km).
First, we need to convert the distance from meters to kilometers:
1.9 x 10^7 m = 19 x 10^6 m = 19,000 km
So, the distance between the center of the Earth and the 0.70 kg mass is 25,484 km - 19,000 km = 6,484 km.
Now we can plug in the values into the formula:
F = G * (m1 * m2) / r^2
F = (6.67 x 10^-11 N m^2/kg^2) * (5.97 x 10^24 kg * 0.70 kg) / (6,484 km * 1000 m/km)^2
F = 2.17 x 10^-1 N
Therefore, the force of gravity on the 0.70 kg mass if it were 1.9 x 10^7 m above Earth's surface would be approximately 0.217 N.
A flat puck (mass M) is rotated in a circle on a frictionless air-hockey tabletop, and is held in this orbit by a light cord connected to a dangling block (mass m) through a central hole in the table as shown in the figure. Start by showing the free-body diagrams and force equations for each mass, and then derive an equation for the tangential speed of the puck. This will be an algebraic expression that includes the variables mentioned above.
The dangling mass will not move and the puck will keep rotating in its orbit, Therefore, V = √(mgR/M) will be an algebraic expression that includes the variables mentioned above.
What is centripetal force?A centripetal force that causes a body to travel along a curved path. The centripetal force always acts orthogonally to the motion of the body and towards the fixed point of the path's instantaneous centre of curvature. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". Gravity is the centripetal force that causes astronomical orbits, according to Newtonian mechanics theory.
A common example of centripetal force is when a body moves at a constant speed along a circular path. The centripetal force is directed at right angles to the motion as well as along the radius of the circular path towards the centre.
Fc = mg
Now, centripetal force on the puck is equal to the mass of the puck times the centripetal acceleration, or
Fc = Mac
centripetal acceleration is related to the tangential velocity of the puck as
ac = V²/R
where R is the radius of the orbit. Then we have
Fc = M ac =M ω² R = M V² / R
and, thus
M V² / R = mg
and, solving for V, we get
V = √(mgR/M)
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An example of kinetic energy continuously being changed to potential energy and back again might be _______.
An example of kinetic energy being continuously changed to potential energy and back again is a swinging pendulum.
When a pendulum is at the highest point in its swing, it has maximum potential energy because it has been lifted to a height above its rest position. At this point, the pendulum is stationary and has no kinetic energy. As the pendulum starts to swing back down, it gains kinetic energy as it accelerates towards the bottom of its swing. As the pendulum reaches the bottom of its swing, it has maximum kinetic energy because it is moving at its fastest speed. As the pendulum starts to swing back up again, it begins to lose kinetic energy as it decelerates against gravity. As the pendulum reaches the highest point of its swing, the process starts all over again, with potential energy being converted to kinetic energy and back again in a continuous cycle. This process will continue until the energy in the system is dissipated due to friction and other forms of resistance, eventually causing the pendulum to come to a stop.
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How to solve this problem
The displacement vectors in component form are A = 1.732 km i + 1 km j and B = -2.955 km i - 0.522 km j.
The distance from home when cell phone rings is 1.309 km.
The direction from home when phone rings is 21.48° West of South.
How to express displacement vectors?(a) The displacement vector A can be expressed in component form as:
A = 2 km [cos(30°) i + sin(30°) j] = 2 km [√3/2 i + 1/2 j] ≈ 1.732 km i + 1 km j
The displacement vector B can be expressed in component form as:
B = 3 km [cos(280°) i + sin(280°) j] = 3 km [-0.985 i - 0.174 j] ≈ -2.955 km i - 0.522 km j
(b) The total displacement vector (C) is the sum of vectors A and B, which can be found by adding the corresponding components:
C = A + B = (1.732 - 2.955) km i + (1 - 0.522) km j = -1.223 km i + 0.478 km j
The magnitude of the resulting vector C can be found using the Pythagorean theorem:
|C| = √((-1.223)² + (0.478)²) ≈ 1.309 km
Therefore, you are about 1.309 km away from home when your cell phone rings.
(c) The direction of the resulting vector C can be found using the inverse tangent function:
θ = tan^-1(0.478/-1.223) ≈ -21.48°
Since the direction is measured with respect to the positive x axis, the direction from "home" to "you" when the phone rings is about 21.48° West of South.
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An artillery shell is fired with an initial velocity of 300 m/s at 55.5° above the horizontal. To clear an avalanche, it explodes on a mountainside 47.0 s after firing. What are the x- and y-coordinates of the shell where it explodes, relative to its firing point?
The x-coordinate of the shell where it explodes, relative to its firing point, is approximately 7688.1 meters, and the y-coordinate is approximately 9507.8 meters.
Is initial velocity always 0?If an automobile is at rest, its beginning velocity is 0.The starting velocity of an automobile that stops after using the brakes will be greater than zero, but the ultimate velocity will be zero.
The kinematic equations of motion can be used to resolve this issue.We can break down the initial velocity into its x- and y-components:
Vx = V0 cosθ = (300 m/s) cos(55.5°) ≈ 163.3 m/s
Vy = V0 sinθ = (300 m/s) sin(55.5°) ≈ 247.2 m/s
Next, we can use the equations of motion to find the shell's position after 47.0 seconds. The x-coordinate is given by:
x = Vx t = (163.3 m/s)(47.0 s) ≈ 7688.1 m
The y-coordinate is given by:
y = Vy t + (1/2)gt²= (247.2 m/s)(47.0 s) + (1/2)(9.81 m/s²)(47.0 s) ≈ 9507.8 m
where g is the acceleration due to gravity.
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What physical characteristics protect animals from forces?
Question 8 options:
cartilage
bones
shells
skin
nose
ears
Bones are physical characteristics that protect animals from forces.
Photons and photon flux a. Consider a 1 kW AM radio transmitter at 700 kHz. Calculate the number of photons emitted fro-m the antenna per second. b. The average intensity of sunlight on Earth's surface is about 1 kW m^-2. The maximum intensity is at a wavelength of around 800 nm. Assuming that all the photons have an 800 nm wavelength, calculate the number of photons arriving on Earth's surface per unit time per unit area. What is the magnitude of the electric field in the sunlight? c. Suppose that a solar cell device can convert each sunlight photon into an electron, which can then give rise to an external current. What is the maximum current that can be supplied per unit area (m^2) of this solar cell device?
The number of photons emitted per second is 2.16 x 10^28 photons/s. The magnitude of the electric field in the sunlight is 3.22 x 10^-5 V/m. The maximum current that can be supplied per unit area by the solar cell device is 1.29 microamperes per square meter.
How to find number of photons emitted per second?a. The energy of a single photon is given by E = hf, where h is Planck's constant and f is the frequency. We can find the frequency of the radio wave as follows:
f = 700 kHz = 700,000 Hz
The energy of a single photon at this frequency is:
E = hf = (6.626 x 10^-34 J s) x (700,000 Hz) = 4.64 x 10^-26 J
The power of the transmitter is 1 kW = 1000 J/s. Therefore, the number of photons emitted per second is:
(1000 J/s) / (4.64 x 10^-26 J/photon) = 2.16 x 10^28 photons/s
b. The energy of a photon with a wavelength of 800 nm can be calculated using the formula E = hc/λ, where h is Planck's constant, c is the speed of light, and λ is the wavelength.
We can then calculate the number of photons arriving on Earth's surface per unit time per unit area as follows:
E = hc/λ = (6.626 x 10^-34 J s) x (3.00 x 10^8 m/s) / (800 x 10^-9 m) = 2.48 x 10^-19 J
The number of photons arriving per unit time per unit area (i.e., the photon flux) is given by the intensity I divided by the energy of a single photon:
I = 1 kW/m^2 = 1000 J/s/m^2
Photon flux = I/E = (1000 J/s/m^2) / (2.48 x 10^-19 J/photon) = 4.03 x 10^21 photons/s/m^2
The magnitude of the electric field in the sunlight can be found using the formula I = ε0cE^2/2, where ε0 is the permittivity of free space and c is the speed of light:
E = sqrt(2I/ε0c) = sqrt(2 x 1000 J/s/m^2 / (8.85 x 10^-12 F/m x 3.00 x 10^8 m/s)) = 3.22 x 10^-5 V/m
c. The maximum current that can be supplied per unit area by the solar cell device is equal to the photon flux multiplied by the charge of an electron (q) and the efficiency of the solar cell (η):
I = ηqPhoton flux = ηq(4.03 x 10^21 photons/s/m^2)
The charge of an electron is q = 1.602 x 10^-19 C, and the efficiency of a typical silicon solar cell is around 20%. Therefore:
I = 0.2 x (1.602 x 10^-19 C) x (4.03 x 10^21 photons/s/m^2) = 1.29 x 10^-6 A/m^2
So, the maximum current that can be supplied per unit area by the solar cell device is 1.29 microamperes per square meter.
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Long wavelength visible light
will have a greater energy than
short wavelength visible light.
will have a speed that is faster than short wavelength light.
has a higher frequency than short wavelength visible light.
will appear blue in color to the average human eye.
will appear red in color to the average human eye.
Longer wavelength visible lights generally have low frequency and energy as compared to shorter wavelength visible lights. This is because the wavelength is inversely proportional to energy and frequency.
What wavelength of light is visible to the human eye?The visible light spectrum is the segment of the electromagnetic spectrum that the human eye can view with unaided eyes. This range of wavelengths is called visible light. Typically, the human eye can easily detect wavelengths from 380 to 700 nanometers.
These wavelengths of light are perceived through the human eyes with the help of specific kinds of cells, that are known as rod and cone cells. special cells called rods and cones live in the retina. These cells are the eye's lookouts. Different rods and cones react to different wavelengths, or colors, of light.
Therefore, longer wavelength visible lights generally have low frequency and energy as compared to shorter wavelength visible lights.
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