To find the velocity of an 11-kilogram object with 792 joules of kinetic energy, we'll use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2}mv^2 \][/tex]
We rearrange this formula to solve for velocity [tex]\( v \)[/tex]:
[tex]\[ v = \sqrt{\frac{2KE}{m}} \][/tex]
Now, let's plug in the given values:
- [tex]\( KE = 792 \)[/tex] joules
- [tex]\( m = 11 \)[/tex] kilograms
Substitute these values into the formula:
[tex]\[ v = \sqrt{\frac{2 \times 792}{11}} \][/tex]
Simplify the expression inside the square root:
[tex]\[ v = \sqrt{\frac{1584}{11}} \][/tex]
Calculate the division:
[tex]\[ v = \sqrt{144} \][/tex]
Now, take the square root of 144:
[tex]\[ v = 12 \][/tex]
Therefore, the velocity of the object is [tex]\( 12 \, \text{m/s} \)[/tex].
The correct answer is:
E. [tex]\( 12 \, \text{m/s} \)[/tex]
