To find the velocity of the ball given its kinetic energy and mass, we use the formula for kinetic energy in terms of velocity:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass,
- [tex]\( v \)[/tex] is the velocity.
We are given:
- [tex]\( KE = 100 \)[/tex] joules,
- [tex]\( m = 2 \)[/tex] kilograms.
First, let's solve for [tex]\( v \)[/tex] by isolating it on one side of the equation. From the formula [tex]\( KE = \frac{1}{2} m v^2 \)[/tex]:
1. Multiply both sides by 2 to eliminate the fraction:
[tex]\[ 2 \cdot KE = m v^2 \][/tex]
This simplifies to:
[tex]\[ 200 = 2 v^2 \][/tex]
2. Divide both sides by [tex]\( m \)[/tex] to solve for [tex]\( v^2 \)[/tex]:
[tex]\[ \frac{200}{2} = v^2 \][/tex]
This simplifies to:
[tex]\[ 100 = v^2 \][/tex]
3. Finally, take the square root of both sides to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{100} \][/tex]
[tex]\[ v = 10 \, \text{m/s} \][/tex]
Therefore, the correct answer is:
E. [tex]\( 10 \, \text{m/s} \)[/tex]
