Sure! Let's solve the problem step by step using the given formula for kinetic energy:
The given information is:
- Velocity [tex]\( v = 50 \, \text{m/s} \)[/tex]
- Kinetic energy [tex]\( KE = 500 \, \text{J} \)[/tex]
The formula for kinetic energy is:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
We need to find the mass [tex]\( m \)[/tex] of the soccer ball.
First, rearrange the formula to solve for [tex]\( m \)[/tex]:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Multiply both sides by 2 to get rid of the fraction:
[tex]\[ 2 KE = m v^2 \][/tex]
Now, solve for [tex]\( m \)[/tex]:
[tex]\[ m = \frac{2 KE}{v^2} \][/tex]
Substitute the given values [tex]\( KE = 500 \, \text{J} \)[/tex] and [tex]\( v = 50 \, \text{m/s} \)[/tex]:
[tex]\[ m = \frac{2 \times 500 \, \text{J}}{(50 \, \text{m/s})^2} \][/tex]
Simplify the expression:
[tex]\[ m = \frac{1000 \, \text{J}}{2500 \, \text{m}^2/\text{s}^2} \][/tex]
[tex]\[ m = 0.4 \, \text{kg} \][/tex]
Therefore, the mass of the soccer ball is [tex]\( 0.4 \, \text{kg} \)[/tex].
So, the correct answer to the question is:
[tex]\[ 0.4 \, \text{kg} \][/tex]
