To find the minimum and maximum coefficient of restitution (COR) for a FIFA Approved soccer ball, we can use the formula for coefficient of restitution:
\[ \text{Coefficient of Restitution (COR)} = \sqrt{\frac{\text{Rebound height}}{\text{Drop height}}} \]
A) Minimum COR:
Given that the ball must bounce at least 135 cm high when dropped from a height of 200 cm onto a steel plate, we can use the formula to find the minimum COR:
\[ \text{Minimum COR} = \sqrt{\frac{135}{200}} \]
\[ \text{Minimum COR} = \sqrt{0.675} \]
\[ \text{Minimum COR} \approx 0.8227 \]
B) Maximum COR:
Similarly, given that the ball must bounce no more than 155 cm high when dropped from a height of 200 cm onto a steel plate, we can use the formula to find the maximum COR:
\[ \text{Maximum COR} = \sqrt{\frac{155}{200}} \]
\[ \text{Maximum COR} = \sqrt{0.775} \]
\[ \text{Maximum COR} \approx 0.8809 \]
Therefore, the minimum coefficient of restitution of a FIFA Approved soccer ball is approximately 0.8227, and the maximum coefficient of restitution is approximately 0.8809.
