To determine the mass of the object, we can use the kinetic energy formula:
[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.
Given:
[tex]\[
KE = 480 \, \text{J}
\][/tex]
[tex]\[
v = 8 \, \text{m/s}
\][/tex]
We need to solve for [tex]\( m \)[/tex]. Let's rearrange the formula to isolate [tex]\( m \)[/tex]:
[tex]\[
KE = \frac{1}{2} m v^2
\][/tex]
Multiply both sides of the equation by 2 to get rid of the fraction:
[tex]\[
2 \times KE = m \times v^2
\][/tex]
[tex]\[
2 \times 480 = m \times (8)^2
\][/tex]
Which simplifies to:
[tex]\[
960 = m \times 64
\][/tex]
Now, solve for [tex]\( m \)[/tex] by dividing both sides by 64:
[tex]\[
m = \frac{960}{64}
\][/tex]
[tex]\[
m = 15 \, \text{kg}
\][/tex]
So the mass of the object is:
[tex]\[
\boxed{15 \, \text{kg}}
\][/tex]
Therefore, the correct answer is 15 kg.
