To calculate the kinetic energy (KE) of the bowling ball, you can use the formula:
\[ KE = \frac{1}{2} mv^2 \]
where:
- \( m \) is the mass of the bowling ball (6 kg),
- \( v \) is the velocity of the bowling ball (7.6 m/s).
Plugging in the values:
\[ KE = \frac{1}{2} \times 6 , \text{kg} \times (7.6 , \text{m/s})^2 \]
Calculating \( (7.6 , \text{m/s})^2 \):
\[ (7.6)^2 = 57.76 , \text{m}^2/\text{s}^2 \]
Now substituting that back into the KE formula:
\[ KE = \frac{1}{2} \times 6 , \text{kg} \times 57.76 , \text{m}^2/\text{s}^2 \]
\[ KE = 3 , \text{kg} \times 57.76 , \text{m}^2/\text{s}^2 \]
\[ KE = 173.28 , \text{J} \]
Thus, the kinetic energy when the bowling ball hits the pin is 173.28 J.
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