   Chapter 5, Problem 22P

Chapter
Section
Textbook Problem

A 60.0-kg athlete leaps straight up into the air from a trampoline with an initial speed of 9.0 m/s. The goal of this problem is to find the maximum height she attains and her speed at half maximum height. (a) What are the interacting objects and how do they interact? (b) Select the height at which the athlete’s speed is 9.0 m/s as y = 0. What is her kinetic energy at this point? What is the gravitational potential energy associated with the athlete? (c) What is her kinetic energy at maximum height? What is the gravitational potential energy associated with the athlete? (d) Write a general equation for energy conservation in this case and solve for the maximum height. Substitute and obtain a numerical answer. (e) Write the general equation for energy conservation and solve for the velocity at half the maximum height. Substitute and obtain a numerical answer.

(a)

To determine
The interacting objects and how do they interact.

Explanation

When the athlete jumps and when he is in the air, the interacting objects are the athlete and the earth. The gravitational force between the athlete and the earth will be the interaction between the objects...

(b)

To determine
The kinetic energy and the gravitational potential energy of the athlete at h=0 level.

(c)

To determine
The kinetic energy and the gravitational potential energy of the athlete at maximum height.

(d)

To determine
The general equation for energy conservation and the maximum height and find the numerical answer for maximum height.

(e)

To determine
The general equation for energy conservation and the velocity at half the maximum height and find the numerical answer for the same.

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