To find the difference in kinetic energy of the bowling ball at the two different speeds, we will use the formula for kinetic energy:
\[ KE = \frac{1}{2}mv^2 \]
where \( m \) is the mass (6 kg) and \( v \) is the velocity.
First, we find the kinetic energy at 16 mph (7.1 m/s):
\[ KE_{16} = \frac{1}{2} \cdot 6 , \text{kg} \cdot (7.1 , \text{m/s})^2 \]
Calculating the velocity squared:
\[ (7.1 , \text{m/s})^2 = 50.41 , \text{m}^2/\text{s}^2 \]
Now, calculate the kinetic energy:
\[ KE_{16} = \frac{1}{2} \cdot 6 \cdot 50.41 = 3 \cdot 50.41 = 151.23 , \text{J} \]
Next, we find the kinetic energy at 14 mph (6.2 m/s):
\[ KE_{14} = \frac{1}{2} \cdot 6 , \text{kg} \cdot (6.2 , \text{m/s})^2 \]
Calculating the velocity squared:
\[ (6.2 , \text{m/s})^2 = 38.44 , \text{m}^2/\text{s}^2 \]
Calculate the kinetic energy:
\[ KE_{14} = \frac{1}{2} \cdot 6 \cdot 38.44 = 3 \cdot 38.44 = 115.32 , \text{J} \]
Now, find the difference in kinetic energy:
\[ \Delta KE = KE_{16} - KE_{14} = 151.23 , \text{J} - 115.32 , \text{J} = 35.91 , \text{J} \]
Thus, the difference in kinetic energy is approximately \( 35.9 , \text{J} \).
The correct answer is:
35.9 J