Question

HELPP THANK YOU!

A 1.0 kg ball is bounced high in the air. What is its total kinetic energy when it reaches its highest point?


a. 40.5 joules
b. 30.0 joules
c. 100.0 joules
d. 50.0 joules
e. 0 joules

Answer 1

The kinetic energy of the ball would be
`0\; {\rm J}` when the ball is at the highest point of the trajectory.

Step-by-step explanation:

The gravitational potential energy of the ball is proportional to the height of the ball. The kinetic energy of the ball is proportional to the square of the speed of the ball.

The total mechanical energy of the ball is equal to the sum of the gravitational potential energy and the kinetic energy of the ball.

Refer to the diagram attached. The horizontal axis denotes time while the vertical axis denotes energy. The three curves are on the same scale.

The ball starts with no gravitational potential energy while it was on the ground. However, the velocity of the ball and the kinetic energy of the ball would be at a maximum.

As the ball moves up along its trajectory, the kinetic energy of the ball would be gradually turned into gravitational potential energy. Hence, the height of the ball increases.

There would be a point where the entirety of the kinetic energy of the ball was turned into gravitational potential energy. The kinetic energy of the ball would be
`0\; {\rm J}`. It would not be possible to further increase the gravitational potential energy of the ball. The ball would thus have reached its maximum height.

After reaching the highest point, the ball would start moving back to the ground. Gravitational potential energy of the ball would be turned back into kinetic energy. As a result, the height of the ball would decrease while the velocity of the ball would increase.

Thus, the kinetic energy of the ball would be
`0\; {\rm J}` when the ball is at maximum height.