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