To calculate the kinetic energy (KE) of the bowling ball, we can use the formula:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \(m\) is the mass (in kilograms),
- \(v\) is the velocity (in meters per second).
Given:
- \(m = 6\) kg,
- \(v = 7.6\) m/s.
Now, substituting the values into the formula:
\[ KE = \frac{1}{2} \times 6 , \text{kg} \times (7.6 , \text{m/s})^2 \]
First, calculate \( (7.6 , \text{m/s})^2 \):
\[ (7.6)^2 = 57.76 , \text{m}^2/\text{s}^2 \]
Now, substitute this back into the formula:
\[ KE = \frac{1}{2} \times 6 \times 57.76 \]
Calculating \( \frac{1}{2} \times 6 = 3 \):
\[ KE = 3 \times 57.76 = 173.28 , \text{J} \]
Therefore, the kinetic energy of the bowling ball when it hits the pin is:
173.28 J