a ball is projected into the air. describe the change(s) in potential and kinetic energy.\na potential…

a ball is projected into the air. describe the change(s) in potential and kinetic energy.\na potential energy decreases and kinetic energy increases.\nb kinetic energy increases and potential energy decreases.\nc potential energy decreases while kinetic energy increases; then kinetic energy decreases and potential energy increases.\nd kinetic energy decreases as potential energy increases; once at the top, the potential energy decreases as kinetic energy increases.

a ball is projected into the air. describe the change(s) in potential and kinetic energy.\na potential energy decreases and kinetic energy increases.\nb kinetic energy increases and potential energy decreases.\nc potential energy decreases while kinetic energy increases; then kinetic energy decreases and potential energy increases.\nd kinetic energy decreases as potential energy increases; once at the top, the potential energy decreases as kinetic energy increases.

Answer

Explanation:

Step1: Recall energy - conservation concepts

The total mechanical energy (E = K+U) (kinetic energy (K=\frac{1}{2}mv^{2}) and potential energy (U = mgh)) is conserved in the absence of non - conservative forces (neglecting air resistance here).

Step2: Analyze the upward motion

As the ball is projected upwards, its height (h) increases and its velocity (v) decreases. Since (U=mgh) and (K = \frac{1}{2}mv^{2}), the potential energy (U) increases and the kinetic energy (K) decreases.

Step3: Analyze the downward motion

At the maximum height, the velocity (v = 0) (momentarily), so (K=0) and (U) is maximum. As the ball falls back down, its height (h) decreases and its velocity (v) increases. So, the potential energy (U) decreases and the kinetic energy (K) increases.

Answer:

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