Question

in the example, the final kinetic energy is determined to be ____________ because at the peak height, the ball instantaneously stops.
a positive
b zero
c negative

in this system, potential and kinetic energy are ____________ proportional.
a inversely
b directly

Explanation:

• For the first question: Kinetic energy formula is \(K = \frac{1}{2}mv^{2}\). At the peak height, the ball's velocity \(v = 0\). Substituting \(v = 0\) into the formula gives \(K=\frac{1}{2}m\times0^{2}=0\).
• For the second question: In a conservative system (assuming no non - conservative forces like air resistance), the total mechanical energy \(E = K+U\) (where \(K\) is kinetic energy and \(U\) is potential energy) is constant. As the ball goes up, \(K\) decreases and \(U\) increases and vice - versa. So, they are inversely proportional.

Answer:

1. B. zero
2. A. inversely