The coefficient of restitution, e, is a measurement developed by Newton that is

Question

The coefficient of restitution, e, is a measurement developed by Newton that is commonly used in sports such as golf, tennis, and basketball. This coefficient of a bouncing ball or object is defined as the ratio of speed right after impact to speed right before impact.
A) Derive a formula for the coefficient of restitution for a ball released from an initial height h0 that rebounds to a final height h in terms of the variables h and h0.
B) Calculate e for a golf ball that bounces to a height of 60 cm from a release height of 83 cm.
C) The upper allowed limit for e for a golf club is 0.83. If the data in part (b) was measured by bouncing it off of a golf driver, was the driver legal?

Explanation / Answer

(A) converting height into equivalent speed,

v = sqrt(2gh)

e = velocity of separation / velocity of approach

e = sqrt(2 gh ) / sqrt(2 g h0) = sqrt(h/h0)

(B) e = sqrt(0.60 / 0.83) = 0.85

(C) that is more than allowed limit.

no it was not legal.

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