To find the velocity of an 11-kilogram object with 792 joules of kinetic energy, we can use the formula for kinetic energy, which relates the kinetic energy (KE), mass (m), and velocity (v):
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
We are given:
- [tex]\( KE = 792 \)[/tex] joules,
- [tex]\( m = 11 \)[/tex] kilograms.
We need to solve for [tex]\( v \)[/tex]. First, we rearrange the formula to solve for [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{\frac{2 KE}{m}} \][/tex]
Next, substitute the given values into the formula:
[tex]\[ v = \sqrt{\frac{2 \times 792}{11}} \][/tex]
Simplify inside the square root:
[tex]\[ v = \sqrt{\frac{1584}{11}} \][/tex]
[tex]\[ v = \sqrt{144} \][/tex]
Finally, we take the square root of 144:
[tex]\[ v = 12 \, \text{m/s} \][/tex]
Therefore, the correct answer is:
E. [tex]\( 12 \, \text{m/s} \)[/tex]
