Frici the cat has excellent hearing. He hears the tapping of his favorite treat from afar
in his plate in front of the door.
His owner dropped the treat into his plate from a height of 125 cm, the door is 30 meters from the garden gate, Frici
and he was wandering at the edge of the forest 300 meters from the garden entrance. Its reaction time is 0.1 seconds and 6.6
is speeding home at a speed of m/s.
How long after dropping the reward snack does Frici arrive if the speed of sound is 330 m/s?
Help:
Sub-question 1: How long will the reward wall fall if the difficulty acceleration is set to 10 m/s²
shall we round?
Sub-question 2: How long does it take for the voice to reach Frici?
Sub-question 3: How long does it take Frici The cat to reach her plate?

At a mass that is 2 times the current earth and a radius 5 times its value, your weight will be 52.8 N.

In general, we can assume a gravitational force of the following magnitude for any planet or mass:

[tex]F = \frac{Gm_{1} m_{2} }{r^{2} }[/tex]

where G = 6.67 x 10⁻¹¹m³/kgs², a universal gravitational constant.

m = masses of objects

r = radius of objects.

Given that W = 660 N

m₁ = 2Me, new mass of earth

r = 5re, new radius of earth

Then [tex]660 N = \frac{GM_{E} m}{r^{2}_{E} }[/tex]

Since [tex]F = \frac{GM m}{r^{2} }[/tex]

Substituting both new mass and radius;

[tex]F = \frac{G(2M_{E}) m}{(5r_{E})^{2}}[/tex]

[tex]F = \frac{2}{25} \frac{GM_{E} m}{r^{2}_{E}}[/tex]

Using the equation that  weight is [tex]660 N = \frac{GM_{E} m}{r^{2}_{E} }[/tex]

[tex]F = \frac{2}{25}(660 N)[/tex] = 0.08 x 660 N

F = 52.8 N

Since the earth is 5 times its radius and twice its mass a weight of 650N will become 52.8 N.

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The correct product of the above nuclear reaction is 221/87 Fr (option C).

A nuclear reaction is the process such as the fission of an atomic nucleus, or the fusion of one or more atomic nuclei and/or subatomic particles in which the number of protons and/or neutrons in a nucleus changes.

In a nuclear reaction, the reaction products may contain a different element or a different isotope of the same element.

Alpha decay is a specific type of nuclear reaction in which an alpha particle made up of helium-4 atom (consisting of two protons and two neutrons), is emitted.

According to this question, the nuclear reaction (alpha decay) of an atom with mass number 225 and atomic number 89 is given. To find the mass number and atomic number of the product, we subtract 4 and 2 respectively.

Therefore, option C is correct.

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Answer:

130 N

Explanation:

g is directly proportional to the mass of the planet (M) and indirectly proportional to the square of the radius of the planet (R²).

g = GM/R²

G = gravitational constant

Therefore if Earth increases in mass by X5 and increases in radius by X5, then the value of g (9.8 m/s²) changes by a factor of 5/5² = 5/25 = 1/5.

Weight = W = mg

(650N)(1/5) = 130 N

Answer:

[tex]\Delta P \approx 7.2 \ N/cm^2}[/tex]

Explanation:

To calculate the difference in pressure that Alexa exerts on the ground when wearing high-heeled shoes compared to when she has bare feet, we can use the following formula for pressure:

[tex]\rightarrow P=\dfrac{F}{A}[/tex]

Where:

First, let's calculate the pressure when Alexa is wearing high-heeled shoes:

F = 560 N (given)

A = 58 cm² (given)

[tex]P_h=\dfrac{560}{58}\\\\\\\\\therefore P_h \approx 9.655 \ N/cm^2[/tex]

Next, let's calculate the pressure when Alexa has bare feet:

F = 560 N (given)

A = 230 cm² (given)

[tex]P_b=\dfrac{560}{230}\\\\\\\\\therefore P_h \approx 2.435 \ N/cm^2[/tex]

Finally, let's calculate the difference in pressure:

[tex]\Delta P= P_h-P_b\\\\\\\\\Longrightarrow \Delta P =9.655-2.435\\\\\\\\\therefore \boxed{\boxed{\Delta P \approx 7.2 \ N/cm^2}}[/tex]

Therefore, the difference in pressure that Alexa exerts on the ground when wearing high-heeled shoes compared to when she has bare feet is approximately 7.2 N/cm².

Answer:

The magnitude and direction of the net force acting on the ring is equal to the vector sum of the three forces acting on it. Based on the figure, the net force acting on the ring is equal to the vector sum of F1 minus F2 plus F3, and its magnitude is equal to the square root of (F1^2 + F3^2) minus (F2^2). The direction of the net force is the same as that of F1 minus F2 plus F3. This is because the three forces, F1, F2, and F3, all act concurrently and will add up to produce a single resultant, or net force.

The magnitude and direction of the net electric force on each of the spheres is 1.92 x 10⁻⁵ N to the right.

The net electric force on the charges is calculated as follows;

F (net) = F (AB) + F (BC)

where;

The electric force between sphere A and B is calculated as follows;

F ( AB ) = kq₁q₂ / r²

where;

F (AB) = ( 9 x 10⁹ x 5.1 x 10⁻⁹ x 1.6 x 10⁻⁹ ) / ( 0.03² )

F (AB) = 8.16 x 10⁻⁵

since it is between two positive charges, it will be repulsive, hence F (AB) = - 8.16 x 10⁻⁵

The electric force between sphere B and C is calculated as follows;

F (BC) = ( 9 x 10⁹ x 2.8 x 10⁻⁹ x 1.6 x 10⁻⁹ ) / ( 0.02² )

F (BC) = 1.008 x 10⁻⁴ N

since the force is between opposite charges, it will attractive, so F (BC) is positive.

The net force on each sphere is calculated as;

F (net) =  -8.16 x 10⁻⁵ N +  1.008 x 10⁻⁴ N

F (net) = 1.92 x 10⁻⁵ N

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Answer:

f = 1219/min = 1219 / 60 / sec = 20.32 / sec

T = 1/f = 1 / 20.32 = .04922 sec      period of 1 revolution

t = 12.9 / 360 * .04922 = .001764 sec    time to pass between disks

V = S / t = .97 m / .001764 = 550 m/sec

The result of the ratio of the displacement module of the second body at the point of meeting is 0.5.

To determine the ratio of the displacement of the first body to the displacement of the second body at the moment of their meeting, use the equation of motion:

d = vt + 1/2at²

where d is the displacement, v is the initial velocity, t is the time, and a is the acceleration.

Since the bodies are moving simultaneously towards each other, then assume that their initial velocities are zero. Also, at the moment of their meeting, their displacement will be the same, d₁ = d₂.

Assume that the time at which they meet is t, then:

d₁ = 1/2 * 2.4t²

And the equation for the displacement of the second body:

d₂ = 1/2 * 4.8t²

If d₁ = d₂

then, 1/2 * 2.4t² = 1/2 * 4.8t²

Solving this equation for t and substituting it into the equation for d₁ or d₂, the ratio of the displacement of the first body to the displacement of the second body: d₁/d₂ = 2.4/4.8 = 0.5 or 1/2

So, at the moment of their meeting, the displacement of the first body is half of the displacement of the second body.

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Answer:

t = 1s is 44 m/s and 72 m/s^2

Explanation:

The distance covered by a car at a time t is given by x=20t+6t^4. To calculate the instantaneous velocity and acceleration when t=1s, we can use the formulas for velocity and acceleration, which are:

Velocity (v) = dx/dt = d/dt(20t+6t^4) = 20 + 24t^3

Acceleration (a) = dv/dt = d/dt(20 + 24t^3) = 72t^2

When t = 1s, we can substitute this value into the formulas for velocity and acceleration:

Velocity (v) = 20 + 24(1)^3 = 20 + 24 = 44 m/s

Acceleration (a) = 72(1)^2 = 72 m/s^2

Therefore, the instantaneous velocity and acceleration of the car when t = 1s is 44 m/s and 72 m/s^2, respectively.

(a) At 20 kHz, the reactance of the inductor is X_L = 2πfL = 2π(20,000 Hz)(20 mH) = 1,256 Ω. The maximum current through the inductor is I_max = V/X_L = 9 V/1,256 Ω = 7.14 mA.

Reactance is an electrical phenomenon that occurs when an alternating current (AC) is applied to an inductive circuit. It is a type of opposition to the flow of electric current due to the inductance of the circuit. Reactance is measured in ohms and is the result of the inductive effect of the circuit components. When an AC voltage is applied to a circuit, the current that flows through the inductive circuit opposes the voltage change and produces an opposing voltage across the inductor which is called reactance.

(b) At 60 Hz, the reactance of the inductor is X_L = 2πfL = 2π(60 Hz)(20 mH) = 377 Ω. The maximum current through the inductor is I_max = V/X_L = 9 V/377 Ω = 23.87 mA. At lower frequencies, the reactance of the inductor is lower, so the current through the inductor is higher.

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Answer:

129.95 N

Explanation:

First, you want to find the acceleration due to gravity on this hypothetical planet.

Using the equation [tex]g = G (M/R^2)[/tex] , where G is a constant ([tex]6.67 * 10^{-11}[/tex]),  M is mass of the planet, and R is radius of the planet, we can plug in the numbers of earth and then multiply them by whatever the question requires, in this case, 5x.

[tex]g = (6.67 * 10^{-11})(5*(5.97 * 10^{24})) /(5* (6.378 *10^{6}))^{2}[/tex]

g = 1.96 m/s. The acceleration due to gravity on this planet is 1.96 m/s.

Now to find your weight.

First, you want to find your mass.

On earth, your weight is equal to your natural force (Fn)

mg = Fn

m(9.8) = 650 ==> mass = 66.33 kg

Now, to find your weight on this hypothetical planet, multiply your mass by the acceleration due to gravity (g)

M x g

66.33 x 1.96 = 129.95 N

You would weigh 129.95 N

The student can conclude that in Experiment 1, the ball is following a parabolic path, demonstrated by the best-fit curve line. In Experiment 2, the ball is following a linear path, demonstrated by the best-fit curve line.

What is curve?
A curve is a line in a two-dimensional plane that is bent or curved. It is often used to describe the shape of objects or mathematical functions. It is often used to study changes in data over time and to understand the behavior of functions and equations. Curves can be described using a variety of mathematical equations and equations can be used to predict the behavior of a curve. Additionally, curves can be used to describe the motion of physical objects and to help visualize the relationships between the objects.

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If the earth is 5 times as massive and the radius 5 times its present value, your weight will be 130 N.

Weight is the amount of gravitational force acting on an object as a result of the gravitational attraction of the Earth.

Assuming gravitational force = [tex]F = \frac{Gm_{1} m_{2} }{r^{2} }[/tex]

where G = 6.67 x 10⁻¹¹m³/kgs², a universal constant.

m = masses of two objects and

r = distance of two objects.

Given that W = 650 N

m₁ = 5Me, new mass of earth

r = 5re, new radius of earth

Then [tex]650 N = \frac{GM_{E} m}{r^{2}_{E} }[/tex]

Let the new weight be [tex]F = \frac{GM m}{r^{2} }[/tex]

Substituting the new mass and radius;

[tex]F = \frac{G(5M_{E}) m}{(5r_{E})^{2}}[/tex]

[tex]F = \frac{5}{25} \frac{GM_{E} m}{r^{2}_{E}}[/tex]

Knowing that [tex]650 N = \frac{GM_{E} m}{r^{2}_{E} }[/tex]

[tex]F = \frac{5}{25}(650 N)[/tex] = 0.2 x 650N

F = 130 N

When the earth is 5 times its radius and 5 times its mass a weight of 650N will become 130 N.

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The gravitational force between them would be twice as much.

option D is the correct answer.

Newton's law of universal gravitation states that the force of attraction between two object in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between the two objects.

Mathematically, the formula for Newton's law of universal gravitation is given as;

F = ( Gm₁m₂ ) / ( R² )

where;

When mass of one of the objects doubles, the new gravitational force will be calculated as;

F' = ( Gm₁ x 2m₂ ) / ( R² )

F' =  2( Gm₁m₂ ) / ( R² )

F' = 2F

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The resultant is the sum of the two displacements having the same direction as the original vectors.

A displacement is described as a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion.

Vectors in the same direction can be simply added to obtain the resultant vector.

We can describe vector as  a term that refers colloquially to some quantities that cannot be expressed by a single number, or to elements of some vector spaces.

In conclusion, If we want to sum two vectors that are collinear and have the same sense, we can make that adding such as an algebraic sum.

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The resultant is the sum of the two displacements having the same direction as the original vectors. Option A

We know that there are generally two kinds of variables that we can be able to have in Physics, we have the scalars and the vectors. In the vectors we have the quantities that have both magnitude and direction while in the scalars we have the quantities that have only magnitude.

We know that when two vectors do have the same direction, we can be able to obtain the resultant vector by addition of the vectors together.

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Answer:

Option a. The baton's center of mass is closer to the larger sphere, making the lever arm distance between your hand and the center of mass longer in option a than in option b. The longer lever arm distance gives you finer control.

Answer:

b) 0.48m is the right answer.

Answer:

C

Explanation:

The system pressure will be equal to 70 pounds divided by the area of the small piston, which is 5.33 square inches. This gives a pressure of 13.13 psi (pounds per square inch).

The distance the car travels before coming to a stop can be calculated using the equation d = (v^2 - u^2)/2a, where v is the initial velocity, u is the final velocity, and a is the acceleration.

What is acceleration?

Acceleration is the rate of change of velocity over time. It is defined as the rate at which an object's speed or direction changes with respect to time. Acceleration is a vector quantity, meaning it has both magnitude and direction.

The SI unit for acceleration is meters per second squared (m/s2). It is also commonly expressed in feet per second squared (ft/s2). Acceleration can be positive, negative, or zero. Positive acceleration occurs when an object increases its speed, and negative acceleration when it decreases its speed. Zero acceleration occurs when an object's speed remains constant.

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The dimensional relation of the time period bob with its length is shown below.

a method of analysis that represents physical quantities in terms of their fundamental dimensions in the absence of enough data to create precise equations.

Dimensional analysis is a method used in engineering and the physical sciences to reduce physical quantities like acceleration, viscosity, and energy to their three basic dimensions of length, mass, and time (T).

[T]=[M^0 L^0 T^1]

[L]=[M^0 L^1 T^0]

[g]=[M^0 L^1 T^-2]

SQUARE ROOT OF (L/g)=[m0l1t0]/[m0l1t-2]

                                         =[m0l0t1]

                                            = R.H.S.

Hence it's dimensionally correct.

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D. Gravity, weak nuclear force, electromagnetic force, strong nuclear force

The four fundamental forces in the universe, in order of increasing magnitude, are:

Gravity: This is the weakest of the four fundamental forces. It is the force that holds everything together and is responsible for the attraction between masses.

Weak Nuclear Force: This force is responsible for certain types of radioactive decay and the fusion of nuclei in stars. It is about 10^25 times weaker than the strong nuclear force.

Electromagnetic Force: This force is responsible for electric and magnetic interactions, such as the forces between charges, the forces between magnets, and the forces between electric currents.

Strong Nuclear Force: This is the strongest of the four fundamental forces. It holds the protons and neutrons in an atom's nucleus together, and it is about 10^38 times stronger than the electromagnetic force.

Therefore, the correct order of the four fundamental forces in terms of increasing magnitude is D: Gravity, weak nuclear force, electromagnetic force, strong nuclear force

Answer:

Explanation:

The speed of the second car after the collision can be found using the law of conservation of momentum. The law states that the total momentum of a system remains constant if no external forces act on it.The initial momentum of the first car is (15g)(22 cm/s) = 330 g cm/s to the right.

The initial momentum of the second car is (22g)(-31 cm/s) = -682 g cm/s to the left.

The total initial momentum of the system is 330 g cm/s - 682 g cm/s = -352 g cm/sAfter the collision, the final momentum of the first car is (15g)(-42 cm/s) = -630 g cm/s to the left.

The final momentum of the second car is (m)(v) where m is the mass of the second car and v is the speed after the collision.

The total final momentum of the system is -630 g cm/s + (m)(v) = -352 g cm/s (since it remains constant)Therefore, m*v = -630 g cm/s + 352 g cm/s = -278 g cm/sTo find v, we need to divide the momentum by the mass

v = -278 g cm/s / 22 g = -12.6 cm/sSo the speed of the second car after the collision is -12.6 cm/s to the left.

Answer:

A. 1

B. n

C. 0

Explanation:

The numbers to the right of the symbols represent the [tex]\frac{mass\ number}{atomic\ number}[/tex].  Recall that the mass number is the sum of the number of neutrons and the number of protons in an atom's nucleus.  The atomic number is the number of protons in an atom's nucleus.  For this equation to be true, both sides must agree on the total number of subatomic particles.  So, for the mass number:

[tex](1+235)=(99+133+4A)\\236=232+4A\\4=4A\\1=A[/tex]

This means the sum of the protons and neutrons in the particle is 1.

For the atomic number:

[tex](0+92)=(41+51+4C)\\92=92+4C\\0=4C\\0=C[/tex]

This means there are 0 protons in the particle.

The two derived values indicate that the particle is a lone neutron.  So, the answer to B is n.

The true statement about  gravitational mass is the more mass an object has, the more gravitational acceleration it will experience.

option B.

The gravitational acceleration of an object is the acceleration an object with mass experiences due to impact of force of gravity on the object.

g = ( GM ) / ( R² )

where;

From the equation given above, the acceleration of an object increases with increase in the mass of the object and decrease in the radius of the object.

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The volume of the cone is 15.7 cm^3.

Density of cone is 0.38 kg/cm^3

Radius of the cone = 3 cm

Height of the cone = 10 cm

Formula used:

Volume of a cone = (1/3) × π × r^2 × h

Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume. Density Symbol D or ρ Density Formula: ρ = m/V, where ρ is the density, m is the mass of the object and V is the volume of the object.

Where, r = radius of the cone

h = Height of the cone

Volume of the cone = (1/3) × π × r^2 × h

(1/3) × π × 3^2 × 10

(1/3) × (22/7) × 3^2 × 10

15.7 cm^3

Density = mass/volume

Density = 6kg/15.7 cm^3

Density = 0.38 kg/cm^3

Hence, the volume of the cone is

15.7 cm^3

And density of cone is 0.38 kg/cm^3

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The momentum of the ball is

(-0.18, -0.40, 0.20)m

Generally, The momentum principle, also known as Newton's second law of motion, states that the rate of change of momentum of an object is equal to the force applied to it. Mathematically, this can be expressed as:

F = d(mv)/dt

where

To determine the position of the ball 0.1 seconds later, we need to know the force acting on the ball due to the elastic band. This force is given by Hooke's Law, which states that the force acting on an object due to a spring is equal to the spring constant (k) multiplied by the displacement of the spring from its relaxed position. In this case, the spring constant is 0.9 N/m, and the displacement is the difference in length between the relaxed length (0.3 m) and the current length of the elastic band.

We know that the ball is at location (-0.2, -0.61, 0)m relative to the point where the elastic band is attached to the paddle. We can find the length of the elastic band by using the distance formula:

√((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2 ) = √((-0.2 - 0)^2 + (-0.61 - 0)^2 + (0 - 0)^2 )

= √(0.04 + 0.3721 + 0)

= √0.4121

= 0.63874m

The displacement of the spring is the relaxed length (0.3 m) minus the current length of the elastic band (0.63874 m), which is -0.33874 m. The force acting on the ball due to the elastic band is

-0.9 * -0.33874 = 0.30486 N.

We can use the force to find the acceleration of the ball using Newton's second law,

F = ma.

Since the mass of the ball is 0.015 kg, the acceleration of the ball is

0.30486 N / 0.015 kg = 20.324 m/s^2

We can use this acceleration to find the final velocity of the ball using the equation vf = vi + at.

Since the initial velocity of the ball is

(-0.02, -0.01, -0.02) kg-m/s, the final velocity of the ball is

(-0.02, -0.01, -0.02) + (20.324, 20.324, 20.324) * 0.1 s = (-0.02, -0.01, -0.02) + (2.0324, 2.0324, 2.0324)

= (2.0124, 2.0224, 2.0124) m/s

The final position of the ball can be found using the equation

xf = xi + vt.

The initial position of the ball is (-0.2, -0.61, 0)m and the final velocity is (2.0124, 2.0224, 2.0124) m/s, so the final position of the ball after 0.1 s is

(-0.2, -0.61, 0) + (2.0124, 2.0224, 2.0124) * 0.1 s

= (-0.2, -0.61, 0) + (0.20124, 0.20224, 0.20124)

= (-0.18, -0.40, 0.20)m

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