Since the initial potential energy and final kinetic energy are zero, our equation now becomes EP,f = EK,i. We can then substitute the formula for kinetic energy, EK = 1/2mv2, and the formula for gravitational potential energy, EP = mgh, mghf = 1/2mvi2. Now it's just a matter of doing the algebra, solving for the final height hf, and substituting values to find hf. Notice that the mass m divides out of both sides of the equation, so the value of the mass is not needed to find the final height. Calculate the maximum height of the ball in meters. hf = __________ m

Since the initial potential energy and final kinetic energy are zero, our equation now becomes EP,f = EK,i. We can then substitute the formula for kinetic energy, EK = 1/2mv2, and the formula for gravitational potential energy, EP = mgh, mghf = 1/2mvi2. Now it's just a matter of doing the algebra, solving for the final height hf, and substituting values to find hf. Notice that the mass m divides out of both sides of the equation, so the value of the mass is not needed to find the final height. Calculate the maximum height of the ball in meters. hf = __________ m

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.17P

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Relativistic Energy and Momentum

According to classical physics, time flow is the same for every observer. But according to einstein's theory, time flow is different for different observers. The idea that time flow is not the same for all may sound strange because we may not experience this effect in everyday life. This effect is only observed when an object moves with some velocity comparable to the velocity of light. This velocity is termed relativistic velocity.

Question

Since the initial potential energy and final kinetic energy are zero, our equation now becomes

E_P,f = E_K,i.

We can then substitute the formula for kinetic energy,

E_K = 1/2mv²,

and the formula for gravitational potential energy,

E_P = mgh,

mgh_f = 1/2mv_i².

Now it's just a matter of doing the algebra, solving for the final height

h_f,

and substituting values to find

h_f.

Notice that the mass m divides out of both sides of the equation, so the value of the mass is not needed to find the final height.

Calculate the maximum height of the ball in meters.

h_f = __________ m

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