To find the velocity of an 11-kilogram object with 792 joules of kinetic energy, we use the formula for kinetic energy and velocity:
[tex]\[ v = \sqrt{\frac{2KE}{m}} \][/tex]
where:
- [tex]\( KE \)[/tex] is the kinetic energy,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( v \)[/tex] is the velocity of the object.
Given:
- [tex]\( KE = 792 \)[/tex] joules,
- [tex]\( m = 11 \)[/tex] kilograms.
Substituting the given values into the formula:
[tex]\[ v = \sqrt{\frac{2 \times 792}{11}} \][/tex]
Simplifying the expression inside the square root:
1. Calculate the numerator:
[tex]\[ 2 \times 792 = 1584 \][/tex]
2. Divide by the mass:
[tex]\[ \frac{1584}{11} = 144 \][/tex]
3. Take the square root:
[tex]\[ \sqrt{144} = 12 \][/tex]
Thus, the velocity [tex]\( v \)[/tex] of the object is:
[tex]\[ 12 \, m/s \][/tex]
Therefore, the correct answer is:
E. [tex]\( 12 \, m/s \)[/tex]
