Question

A couple of soccer balls of equal mass are kicked off the ground at the same speed but at different angles. Soccer ball A is kicked off at an angle slightly above the horizontal, whereas ball B is kicked slightly below the vertical. How do each of the following compare for ball A and ball B? (a) The initial kinetic energy and (b) the change in gravitational potential energy from the ground to the highest point? If the energy in part (a) differs from part (b), explain why there is a difference between the two energies.

a) Ball A has greater initial kinetic energy, and the change in potential energy is greater for ball B.
b) Ball B has greater initial kinetic energy, and the change in potential energy is greater for ball A.
c) Both balls have equal initial kinetic energy and equal changes in potential energy.
d) The relationship between initial kinetic energy and change in potential energy cannot be determined.

Answer 1

Ball A has greater initial kinetic energy, and the change in potential energy is greater for Ball B. The difference between the two energies can be explained by the fact that initial kinetic energy depends on the horizontal velocity component, whereas the change in gravitational potential energy depends on the vertical displacement.

Step-by-step explanation:

When comparing the initial kinetic energy of Ball A and Ball B, Ball A has greater initial kinetic energy.

This is because Ball A is kicked off at an angle slightly above the horizontal, which gives it a greater horizontal velocity component compared to Ball B.

When comparing the change in gravitational potential energy from the ground to the highest point, the change is greater for Ball B.

This is because Ball B is kicked slightly below the vertical, resulting in a higher maximum height compared to Ball A.

The difference between the two energies can be explained by the fact that initial kinetic energy depends on the horizontal velocity component, whereas the change in gravitational potential energy depends on the vertical displacement.