To find the speed of the golf ball given its kinetic energy (KE), we can use the formula for kinetic energy:
\[ KE = \frac{1}{2} m v^2 \]
where:
- \( KE \) is kinetic energy,
- \( m \) is the mass of the object,
- \( v \) is the velocity (speed) of the object.
Rearranging the formula to solve for \( v \):
\[ v = \sqrt{\frac{2 \times KE}{m}} \]
We know that:
- The kinetic energy \( KE = 1433 , J \)
- The mass \( m = 47.0 , g = 0.047 , kg \) (we need to convert grams to kilograms).
Substituting the values into the formula:
\[ v = \sqrt{\frac{2 \times 1433 , J}{0.047 , kg}} \]
Calculating the expression:
\[ v = \sqrt{\frac{2866 , J}{0.047 , kg}} \]
\[ v = \sqrt{61,130.43 , \text{m}^2/\text{s}^2} \]
\[ v \approx 247.15 , \text{m/s} \]
Therefore, the speed of the golf ball is approximately 247.15 m/s.