Question

read through the scenarios below and calculate the predicted change in kinetic energy of the object compared to a 25 kg ball traveling at 8 m/s.
a 1 000 kg ball traveling at 8 m/s would have
kinetic energy
a 10 kg ball traveling at 8 m/s would have
kinetic energy
a 100 kg person falling at 8 m/s would have
kinetic energy.

Explanation:

Step1: Calculate kinetic energy formula

The formula for kinetic energy is \(KE=\frac{1}{2}mv^{2}\), where \(m\) is mass and \(v\) is velocity.
For the \(25\) kg ball: \(KE_{1}=\frac{1}{2}\times25\times8^{2}=\frac{1}{2}\times25\times64 = 800\) J.

Step2: Calculate for \(1000\) kg ball

For the \(1000\) kg ball: \(KE_{2}=\frac{1}{2}\times1000\times8^{2}=\frac{1}{2}\times1000\times64 = 32000\) J.
The ratio \(\frac{KE_{2}}{KE_{1}}=\frac{32000}{800}=40\) times.

Step3: Calculate for \(10\) kg ball

For the \(10\) kg ball: \(KE_{3}=\frac{1}{2}\times10\times8^{2}=\frac{1}{2}\times10\times64 = 320\) J.
The ratio \(\frac{KE_{3}}{KE_{1}}=\frac{320}{800}=0.4\) times.

Step4: Calculate for \(100\) kg person

For the \(100\) kg person: \(KE_{4}=\frac{1}{2}\times100\times8^{2}=\frac{1}{2}\times100\times64 = 3200\) J.
The ratio \(\frac{KE_{4}}{KE_{1}}=\frac{3200}{800}=4\) times.

Answer:

A \(1000\) kg ball: \(40\) times; A \(10\) kg ball: \(0.4\) times; A \(100\) kg person: \(4\) times.