Question

a ball is projected into the air. describe the change(s) in potential and kinetic energy.
potential energy decreases and kinetic energy increases.
kinetic energy increases and potential energy decreases.
kinetic energy decreases as potential energy increases; once at the top, the potential energy decreases as kinetic energy increases.
thermal energy becomes potential energy during the fall.

Explanation:

The formula for kinetic energy is $KE=\frac{1}{2}mv^{2}$ and for gravitational - potential energy is $PE = mgh$. As the ball is projected upwards, its height $h$ increases and its vertical velocity $v$ decreases. So, kinetic energy decreases and potential energy increases. At the top - most point, the vertical velocity is 0, so kinetic energy is minimum and potential energy is maximum. As the ball falls down, its height $h$ decreases and its vertical velocity $v$ increases, so potential energy decreases and kinetic energy increases.

Answer:

Kinetic energy decreases as potential energy increases; once at the top, the potential energy decreases as kinetic energy increases.