Question

1. a 4 kg ball is rolling at 3 m/s. what is its kinetic energy?
2. an arrow with a mass of 0.05 kg leaves a bow at 40 m/s. find its kinetic energy.

Explanation:

Step1: Write the formula for kinetic energy

The formula for kinetic energy is \( KE=\frac{1}{2}mv^{2} \), where \( m \) is the mass and \( v \) is the velocity.

Step2: Substitute the values for problem 9

For problem 9, \( m = 4\ kg \) and \( v=3\ m/s \).
Substitute into the formula: \( KE=\frac{1}{2}\times4\times3^{2} \).
First calculate \( 3^{2}=9 \), then \( \frac{1}{2}\times4 = 2 \), and \( 2\times9=18\ J \).

Step3: Substitute the values for problem 10

For problem 10, \( m = 0.05\ kg \) and \( v = 40\ m/s \).
Substitute into the formula: \( KE=\frac{1}{2}\times0.05\times40^{2} \).
First calculate \( 40^{2}=1600 \), then \( \frac{1}{2}\times0.05=0.025 \), and \( 0.025\times1600 = 40\ J \) (but since this is likely a multiple - choice follow - up, we focus on the method).

Answer:

For problem 9: 18 J. For problem 10: 40 J (but if following the multiple - choice in the image for problem 9, the answer is 18 J).