To calculate the kinetic energy of the shot, we use the formula for kinetic energy:
[tex]\[ KE = \frac{1}{2} m v^2 \][/tex]
where
[tex]\( m \)[/tex] is the mass of the object,
[tex]\( v \)[/tex] is the velocity of the object.
Given:
[tex]\[ m = 4 \, \text{kg} \][/tex]
[tex]\[ v = 9 \, \text{m/s} \][/tex]
Now, substitute the given values into the formula:
[tex]\[ KE = \frac{1}{2} \times 4 \, \text{kg} \times (9 \, \text{m/s})^2 \][/tex]
First, calculate [tex]\( (9 \, \text{m/s})^2 \)[/tex]:
[tex]\[ 9 \, \text{m/s} \times 9 \, \text{m/s} = 81 \, \text{m}^2/\text{s}^2 \][/tex]
Next, multiply this result by the mass:
[tex]\[ 4 \, \text{kg} \times 81 \, \text{m}^2/\text{s}^2 = 324 \, \text{kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
Finally, multiply by [tex]\( \frac{1}{2} \)[/tex]:
[tex]\[ \frac{1}{2} \times 324 \, \text{kg} \cdot \text{m}^2/\text{s}^2 = 162 \, \text{J} \][/tex]
Therefore, the kinetic energy of the shot is:
[tex]\[ \boxed{162} \, \text{joules} \][/tex]
