To find the velocity of a ball given its kinetic energy and mass, we use the formula:
[tex]\[ V = \sqrt{\frac{2 \cdot KE}{m}} \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy
- [tex]\( m \)[/tex] is the mass
In this problem:
- [tex]\( KE = 100 \, \text{joules} \)[/tex]
- [tex]\( m = 2 \, \text{kilograms} \)[/tex]
Now, let's substitute the given values into the formula:
[tex]\[ V = \sqrt{\frac{2 \cdot 100}{2}} \][/tex]
Simplify the expression inside the square root:
[tex]\[ \frac{2 \cdot 100}{2} = \frac{200}{2} = 100 \][/tex]
So, we have:
[tex]\[ V = \sqrt{100} \][/tex]
Taking the square root of 100:
[tex]\[ V = 10 \][/tex]
Therefore, the velocity of the ball is:
[tex]\[ 10 \, \text{m/s} \][/tex]
The correct answer is:
E. [tex]\( 10 \, \text{m/s} \)[/tex]
