A student drops a ball three different times.

Question

The table shows the ball’s kinetic energy upon hitting the ground from different heights.

The student claims that a ball dropped 3.0 meters would have fewer than 96 joules of kinetic energy upon hitting the ground. Is she correct? Why?

She is wrong. The higher the drop, the less kinetic the ball will have upon hitting the ground.

She is wrong. The higher the drop, the more kinetic energy the ball will have upon hitting the ground.

She is right! The higher the drop, the greater kinetic the ball will have upon hitting the ground.

She is right! The higher the drop, the less kinetic energy the ball will have upon hitting the ground.

Answer 1

The correct answer is: She is wrong. The higher the drop, the more kinetic energy the ball will have upon hitting the ground.

When an object is dropped from a height, its potential energy is converted into kinetic energy as it falls. The kinetic energy just before it hits the ground can be calculated using the formula:

\[ KE = mgh \]

where \( KE \) is kinetic energy, \( m \) is the mass of the ball, \( g \) is the acceleration due to gravity (approximately 9.81 m/s²), and \( h \) is the height from which it was dropped.

Since the kinetic energy increases with height, a ball dropped from 3.0 meters would have more kinetic energy upon hitting the ground than if it were dropped from a lower height. Therefore, it is incorrect to claim that it would have fewer than 96 joules of kinetic energy without additional context (such as the mass of the ball).