The student says that a ball dropped from a height of 3.0 meters would have less than 96 joules of kinetic energy when it hits the ground. Is she correct and why?

Answer 1

To determine if the student is correct, we can use the formula for gravitational potential energy:

Potential energy (PE) = mass (m) * gravity (g) * height (h)

Since the student mentioned that the ball was dropped, we can assume that it has negligible initial velocity, thus the initial kinetic energy is 0 joules. The potential energy at the height of 3.0 meters would be:

PE = m * g * h

Given that the mass and gravity are constant, we can disregard them for this comparison. Therefore, the potential energy is directly proportional to the height:

PE ∝ h

Since kinetic energy is equal to potential energy when the object is in free fall, we can conclude that the kinetic energy is also directly proportional to the height.

KE ∝ h

Therefore, if the height is reduced, the kinetic energy will also be reduced. In this case, if the ball is dropped from a height of 3.0 meters, the kinetic energy would be less than 96 joules, as stated by the student. Hence, the student's statement is correct.