To find the mass of the soccer ball, we can use the formula for kinetic energy, which is given by:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Here, [tex]\( KE \)[/tex] represents the kinetic energy, [tex]\( m \)[/tex] is the mass of the ball, and [tex]\( v \)[/tex] is its velocity. We are provided with the following values:
- [tex]\( KE = 500 \)[/tex] Joules
- [tex]\( v = 50 \)[/tex] meters per second
To find the mass [tex]\( m \)[/tex], we need to rearrange the kinetic energy formula to solve for [tex]\( m \)[/tex]:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
Multiply both sides of the equation by 2 to get rid of the fraction:
[tex]\[ 2 \cdot KE = m v^2 \][/tex]
Substitute the given values for kinetic energy and velocity:
[tex]\[ 2 \cdot 500 = m \cdot (50)^2 \][/tex]
Calculate [tex]\( (50)^2 \)[/tex]:
[tex]\[ 2 \cdot 500 = m \cdot 2500 \][/tex]
Next, we solve for [tex]\( m \)[/tex] by dividing both sides of the equation by 2500:
[tex]\[ \frac{2 \cdot 500}{2500} = m \][/tex]
Simplify the right-hand side:
[tex]\[ \frac{1000}{2500} = m \][/tex]
[tex]\[ m = 0.4 \][/tex]
Therefore, the mass of the soccer ball is:
[tex]\[ \boxed{0.4 \text{ kg}} \][/tex]
