The student is incorrect.
The kinetic energy (KE) of an object just before it hits the ground can be calculated using the formula:
\[ KE = mgh \]
where:
- \( m \) is the mass of the object,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \)),
- \( h \) is the height from which the object is dropped.
From the data provided, we can observe a clear relationship between the height of the drop and the kinetic energy of the ball. As the height increases, the kinetic energy also increases proportionally.
The student's data shows:
- At 1.0 meters: 48 joules
- At 1.5 meters: 72 joules
- At 2.0 meters: 96 joules
We can see that the kinetic energy increases by an increasing amount as the height increases. To find the kinetic energy for a height of 3.0 meters, we can analyze the pattern in the energy values.
From the data, the increase in height from 1.0 m to 1.5 m (0.5 m increase) results in an increase in kinetic energy of 24 joules (from 48 to 72 joules). The same increase in height (from 1.5 m to 2.0 m) also results in a 24 joules increase (from 72 to 96 joules).
Extending this trend to 3.0 meters, we would expect another increase of 24 joules from 2.0 meters to 3.0 meters:
\[ 96 , \text{joules} + 24 , \text{joules} = 120 , \text{joules} \]
Thus, the kinetic energy of a ball dropped from a height of 3.0 meters would be 120 joules, which is greater than 96 joules. Therefore, the student is incorrect in her assumption that it would have less than 96 joules when it hits the ground.