Question

a basketball player was falling to the ground after dunking the winning basket. at the end of her fall, she was falling at 4 m/s. if she was 60 kg, how much potential energy did she have at the top of her jump? assume all of her potential energy at the top of her jump converted to kinetic energy at the end of her fall.

Explanation:

Step1: Recall the principle of energy conversion

According to the law of conservation of energy, when all potential energy \(U\) is converted to kinetic energy \(K\), we have \(U = K\).

Step2: Use the formula for kinetic energy

The formula for kinetic energy is \(K=\frac{1}{2}mv^{2}\), where \(m = 60\space kg\) (mass of the player) and \(v=4\space m/s\) (velocity at the end of the fall).
Substitute the values into the formula: \(K=\frac{1}{2}\times60\times4^{2}\).
First, calculate \(4^{2}=16\). Then, \(\frac{1}{2}\times60\times16 = 30\times16\).
\(30\times16 = 480\space J\).

Answer:

\(480\space J\)