The student's claim that a ball dropped from 3.0 meters would have fewer than 96 joules of kinetic energy upon hitting the ground is incorrect.
From the data given, we can observe that the kinetic energy (KE) of the ball increases linearly with the height from which it is dropped. The relationship can be represented as follows:
- At 1.0 meters, KE = 48 joules
- At 1.5 meters, KE = 72 joules
- At 2.0 meters, KE = 96 joules
We can calculate the increase in kinetic energy per meter of height:
- From 1.0 m to 1.5 m: an increase of \(72 - 48 = 24\) joules (from 48 to 72 joules)
- From 1.5 m to 2.0 m: an increase of \(96 - 72 = 24\) joules (from 72 to 96 joules)
This suggests that for every 0.5 meters, the kinetic energy increases by 24 joules. If we continue this trend:
- From 2.0 m to 2.5 m: KE would increase by another 24 joules,
- \(96 + 24 = 120\) joules
- From 2.5 m to 3.0 m: KE would increase by another 24 joules,
- \(120 + 24 = 144\) joules
Therefore, a ball dropped from 3.0 meters would have 144 joules of kinetic energy upon hitting the ground, not fewer than 96 joules. Thus, the student's claim is incorrect.