Answer:
h=4+85*time - 1/2 32*time^2
16time^2-85*time-106=0
use the quadratic formula to solve for time (notice two solutions, one going up, one going back down).
time=(85+-sqrt(85^2+4*16*106) )/32
Explanation:
Recheck my work just in case I'm not good at this type of class but I wanted to help.
a. At maximum height h, the baseball has zero vertical velocity, so that with initial velocity v we have
[tex]0^2-v^2 = -2gh \implies h = \dfrac{v^2}{2g}[/tex]
Given that [tex]v = 30 \frac{\rm m}{\rm s}[/tex], the ball reaches a height of
[tex]h = \dfrac{\left(30\frac{\rm m}{\rm s}\right)^2}{2g} \approx \boxed{46\,\mathrm m}[/tex]
b. At max height, the baseball's vertical velocity is such that
[tex]0=v-gt[/tex]
For [tex]v = 30 \frac{\rm m}{\rm s}[/tex], we find
[tex]gt=30\dfrac{\rm m}{\rm s} \implies t = \dfrac{30\frac{\rm m}{\rm s}}g \implies t \approx 3.1 s[/tex]
which is half the time it spends in the air, making the total time about 6.1 s.
c. We saw in part (a) that
[tex]h = \dfrac{v^2}{2g}[/tex]
If we halve the initial speed and replace [tex]v[/tex] with [tex]\frac v2[/tex], we get
[tex]h = \dfrac{\left(\frac v2\right)^2}{2g} = \dfrac14 \cdot \dfrac{v^2}{2g}[/tex]
which means the max height is reduced by a factor of 1/4.
In part (b), we found the time to max height is
[tex]t = \dfrac{v}{g}[/tex]
and halving the initial speed gives
[tex]t = \dfrac{\frac v2}g = \dfrac12 \cdot \dfrac{v}{g}[/tex]
That is, the time to max height is reduced by a factor of 2 when the speed is halved, and so the overall time in the air is reduced by a factor of 2.
10.
Water flows over a section of the
Niagara Falls at a constant rate of about
1.2 X 106 kg/s and falls 50.0 m. How
much power is generated by the falling
water?
Answer: 590 MW
Water flows over a section of Niagara Falls at the rate of 1.2 × 106 kg/s and falls 50 m. How much power is generated by the falling water? = 5.9 × 108 W = 590 MW , where 'MW' represents megawatts.
Explanation:
A grandfather clock is found to gain 60.0 s every 24 hours. If the current length of the pendulum is 0.590 m, how much should the length be changed (in m) to make the clock accurate
Answer:
1.01m
Explanation:
period of pendulum = 2π√l/g
for length .59 m period is 1.54 s
every 24 hrs period increases by 60s or 1 min
except length rest of the components are constant
so the period becomes 2.54 at 24 hrs
for 2.54, the length is 1.601 m
length to be adjusted is 1.6-.59=1.01m
a
a
a
A single charge a produces a
potential Vo = 1000 V at point o
=
0
a
+9
+
a
What is the potential at point o
due to two identical charges as
shown to the right?
a
a
a
O
+9
A) 1000 V
B) 1414 V
C) 2000 V
D) 2828 V
Answer:
C 2000v its obviously ans because if o is 1000 2 vo is 2000v
If a 0.75kg bullet made a 3.0kg block swing to change its height 0.5 Meters. How fast was the bullet traveling? ___ m/s (Round to the tenths)
Answer:
Im Pretty Sure Its 15.7m/s
Explanation:
Hope This Helps tell Me if im wrong
Carbon cycle diagram
Carbon cycle shows is the continous movement of carbon in elemental and combined states on earth.
Steps :-
☆ Carbon moves from the atmosphere to plants. ...
☆ Carbon moves from plants to animals. ...
☆ Carbon moves from plants and animals to soils. ...
☆ Carbon moves from living things to the atmosphere. ...
☆ Carbon moves from fossil fuels to the atmosphere when fuels are burned. ...
☆ Carbon moves from the atmosphere to the oceans.
~ Benhemin360
An aseroid with a mass of 8.4x10^8 kg and a planet with a mass of 6.2x10^23 kg come close to each other by a distance of 8x10^5 m. what is the force of gravity that the asteroid and the planet have on each other ?
So, the force of gravity that the asteroid and the planet have on each other approximately
[tex] \boxed{\sf{5.43 \times 10^{10} \: N}} [/tex]
IntroductionHi ! Now, I will help to discuss about the gravitational force between two objects. We already know that gravitational force occurs when two or more objects interact with each other at a certain distance and generally orbit each other to their center of mass. For the gravitational force between two objects, it can be calculated using the following formula :
[tex] \boxed{\sf{\bold{F = G \times \frac{m_1 \times m_2}{r^2}}}} [/tex]
With the following condition :
F = gravitational force (N)G = gravity constant ≈ [tex] \sf{6.67 \times 10^{-11}} [/tex] N.m²/kg²[tex] \sf{m_1} [/tex] = mass of the first object (kg)[tex] \sf{m_2} [/tex] = mass of the second object (kg)r = distance between two objects (m)Problem SolvingWe know that :
G = gravity constant ≈ [tex] \sf{6.67 \times 10^{-11}} [/tex] N.m²/kg²[tex] \sf{m_1} [/tex] = mass of the first object = [tex] \sf{8.4 \times 10^8} [/tex] kg.[tex] \sf{m_2} [/tex] = mass of the second object = [tex] \sf{6.2 \times 10^{23}} [/tex] kg.r = distance between two objects = [tex] \sf{8 \times 10^5} [/tex]What was asked :
F = gravitational force = ... NStep by step :
[tex] \sf{F = G \times \frac{m_1 \times m_2}{r^2}} [/tex]
[tex] \sf{F = 6.67 \times 10^{-11} \times \frac{8.4 \cdot 10^8 \times 6.2 \cdot 10^{23}}{(8 \times 10^5)^2}} [/tex]
[tex] \sf{F = \frac{347.374 \times 10^{-11 + 8 + 23}}{64 \times 10^10}} [/tex]
[tex] \sf{F \approx 5.43 \times 10^{20 - 10}} [/tex]
[tex] \boxed{\sf{F \approx 5.43 \times 10^{10} \: N}} [/tex]
ConclusionSo, the force of gravity that the asteroid and the planet have on each other approximately
[tex] \boxed{\sf{5.43 \times 10^{10} \: N}} [/tex]
See MoreGravity is a thing has depends on ... https://brainly.com/question/26485200
The cryosphere is a subset of which sphere?
Question 2 options:
Biosphere
Atmosphere
Hydrosphere
Geosphere
Answer:
hydrosphere
Explanation:
the frozen part of the hydrosphere has its own name,the cryosphere
Consider a 1.9 MW power plant (this is the useful output in the form of electric energy) that operates between 30∘C and 450∘C at 65% of the Carnot efficiency. This is enough electric energy for about 750 homes. One way to use energy more efficiently would be to use the 30∘C "waste" energy to heat the homes rather than releasing that heat energy into the environment. This is called cogeneration, and it is used in some parts of Europe but rarely in the United States. The average home uses 70 GJ of energy per year for heating. For estimating purposes, assume that all the power plant's exhaust energy can be transported to homes without loss and that home heating takes place at a steady rate for half a year each year. How many homes could be heated by the power plant?
I don't understand how to solve above question. Hence, please explain it in detail
Up to 230 homes could be heated by the performance of the power plant.
How to calculate the amount of houses benefited by an ideal co-generation plant
By definitions of energy efficiency ([tex]\eta[/tex]), no unit, and principle of energy conservation, the amount of waste heat rate ([tex]\dot Q_{waste}[/tex]), in megawatts, is equal to the difference between the energy input and the useful output, that is to say:
[tex]\dot Q_{waste} = \left(\frac{1}{\eta} -1\right)\cdot \dot E_{out}[/tex] (1)
Where [tex]\dot E_{out}[/tex] is the useful output, in watts.
According to the statement, an average home uses 70 GJ of energy per year for heating and home heating takes place at a steady rate for half a year, then the number of homes ([tex]n[/tex]), no unit, benefited by the co-generation plant is calculated by this formula derived from physical definition of power:
[tex]n = \frac{\dot Q_{waste}\cdot \Delta t}{Q_{home}}[/tex] (2)
Where:
[tex]\Delta t[/tex] - Availability time, in seconds.[tex]Q_{home}[/tex] - Yearly heating consumption, in joules.Now we proceed to find the number of houses: ([tex]\dot E_{out} = 1.9\times 10^{6}\,W[/tex], [tex]\eta = 0.65[/tex], [tex]\Delta t = 1.577\times 10^{7}\,s[/tex], [tex]Q_{home} = 7\times 10^{10}\,J[/tex])
By (1):
[tex]\dot Q_{waste} = \left(\frac{1}{0.65}-1 \right)\cdot (1.9\times 10^{6}\,W)[/tex]
[tex]\dot Q_{waste} = 1.023\times 10^{6}\,W[/tex]
By (2):
[tex]n = \frac{(1.577\times 10^{7}\,s)\cdot (1.023\times 10^{6}\,W)}{7\times 10^{10}\,J}[/tex]
[tex]n = 230.467[/tex]
Up to 230 homes could be heated by the performance of the power plant. [tex]\blacksquare[/tex]
To learn more on co-generation, we kindly invite to check this verified question: https://brainly.com/question/1344306
A crate hangs from a rope that is attached to a metal ring. The metal ring is suspended by a second rope that is attached overhead at two points, as shown. What is the angle if the tension in rope 1 is 0.640 times the tension in rope 2?
We have that the tension in rope 2 is mathematically given as
the tension in rope 2 is
[tex]\theta=71.3[/tex]From the question we are told
A crate hangs from a rope that is attached to a metal ring.
The metal ring is suspended by a second rope that is attached overhead at two points, as shown.
What is the angle if the tension in rope 1 is 0.640 times the tension in rope 2?
Angle of the tensionGenerally the equation for the Tension is mathematically given as
[tex]Tcos\theta+0.640\theta-T_1=0\\\\Therefore\\\\ZTcos \theta-0.640T=0\\\\Cos=0.32\\\\\theta=71.3\\\\[/tex]
Therefore
the tension in rope 2 is
[tex]\theta=71.3[/tex]
For more information on tension visit
https://brainly.com/question/16517842
This is being graded.
Great answers only
Answer:
D.Explanation:
When a ball is at its highest point, its acceleration is 0. The only thing pulling it down, is gravity so, the correct option is D. Downwards.
I'm not sure however due to the fact that the arrows on the other options are facing backwards meaning the ball would go backwards; and for the one option the ball is going up. However, the ball isn't going backwards nor up, so it must be D. If I am wrong I greatly apologize.
A rock is dropped at 10 m height at what speed does it hit the ground?
So, the speed when it (the rock) hit the ground is 14 m/s.
IntroductionHi ! This question will direct you to the "Free Fall Motion" material. Why is that ? This is because there is a keyword "dropped" which means without initial speed and its named free fall motion. Its little bit of different, when the keyword "thrown", that's not a free fall motion. For the equations of velocity in free fall, follow the following equation:
[tex] \boxed{\sf{\bold{v = \sqrt{2 \times g \times h}}}} [/tex] ... (i)
[tex] \boxed{\sf{\bold{v = \sqrt{2 \times g \times (h_1 - h_2)}}}} [/tex] ... (ii)
With the following condition :
v = velocity (m/s)g = acceleration of the gravity (m/s²)h = the height or displacement at vertical line (m)[tex] \sf{h_1} [/tex] = initial high (m)[tex] \sf{h_2} [/tex] = final high (m)Note :
Use the (i) equation when the object has actually touched the ground (the final position of the object is at the ground).Use the (ii) equation when the object not touched the ground (the final position of the object is > 0 m above the ground).Problem SolvingWe know that :
g = acceleration of the gravity = 9.8 m/s²h = the height = 10 m >> The final position of the object is directly touch the ground.What was asked :
v = velocity = ... m/sStep by step :
[tex] \sf{v = \sqrt{2 \times g \times h}} [/tex]
[tex] \sf{v = \sqrt{2 \times 9.8 \times 10}} [/tex]
[tex] \sf{v = \sqrt{196}} [/tex]
[tex] \boxed{\sf{v = 14 \: m/s}} [/tex]
ConclusionSo, the speed when it (the rock) hit the ground is 14 m/s.
See MoreThe speed of the object at a certain height (free fall motion) https://brainly.com/question/26377041The relationship between acceleration and the change in velocity and time in free fall https://brainly.com/question/26486625How many miles is a light year
Answer:
5,878,625,370,000 miles or 5.87 Trillion miles
Explanation:
The result: One light-year equals 5,878,625,370,000 miles (9.5 trillion km).
One light-year equals 5,878,625,370,000 miles (9.5 trillion km)
explanation: To find the distance of a light-year, you multiply this speed by the number of hours in a year (8,766).
27°Celsius to Kelvin 20dg to milligrams and 3 m to decimeter
Answer:
K = C + 273, so 27°C = 27+273 = 300 K
1 dg = 100 mg, so 20 dg = 20×100 = 2,000 mg
Explanation:
Shawn and his bike have a total mass of
43.5 kg. Shawn rides his bike 1.3 km in
10.4 min at a constant velocity.
The acceleration of gravity is 9.8 m/s^2.
What is Shawn’s kinetic energy?
Answer in units of J.
Answer: uhhhhhhhhhhhhhhhhhhhh im responding for points
Explanation:
lololololol sorry
Find the horizontal and vertical components of the following vectors shown in the diagram. In all cases, assume that up and right are positive directions and that the diagonals are 45°.
The horizontal and vertical component of vector A is -3 and 0 respectively.
The horizontal and vertical component of vector B is 0 and 3 respectively.
The horizontal and vertical component of vector C is 0 and 6 respectively.
The horizontal and vertical component of vector D is 4 and 0 respectively.
The horizontal and vertical component of vector E is 3.54 and 3.54 respectively.
The horizontal and vertical component of vector F is -3.54 and -3.54 respectively.
The horizontal an vertical component of each vectorThe horizontal and vertical component of each vector is calculated as follows;
Vector A[tex]A_x = Acos (\theta) = 3 \times cos(180) = -3\\\\A_y = A sin(\theta) = 3 \times sin(180) = 0[/tex]
Vector B[tex]B_x = 3 \times cos(90) = 0\\\\B_y = 3 \times sin(90) = 3[/tex]
Vector C[tex]C_x = 6 \times cos(90) = 0\\\\C_y = 6 \times sin(90) = 6[/tex]
Vector D[tex]D_x = 4 \times cos(0) = 4\\\\D_y = 4 \times sin(0) = 0[/tex]
Vector E[tex]E _x = 5 \times cos (45) = 3.54 \\\\E_y = 5 \times sin(45) = 3.54[/tex]
Vector F[tex]F_x = 5 \times cos(225) = -3.54\\\\F_y = 5 \times sin(225) = -3.54[/tex]
Learn more about component of vectors here: https://brainly.com/question/13416288
Which of the following happens when two positively charged objects are moved away from each other?
the two objects have no influence on each other
the potential energy increases
the potential energy decreases
both a repulsive force and an attractive force is produced
What is the science principle that explains magnetic fields? I need this fast, please!
Answer:
I literally just learned this last week and if I remember correctly it is Faraday's Law of Induction.
Explanation: Hope this helps also I hope you have/had an amazing day today<3
