Question

Assume that according to the official rules of an international sport, a ball acceptable for tournament play must bounce to a height of between 175 and 185 cm when dropped from a height of 254 cm at room temperature. What is the acceptable range of values for the coefficient of restitution for the ball-floor system?

Answer 1

Answer:0.829 to 0.853

Step-by-step explanation:

Given

height through ball is dropped
`h=254 cm`

velocity at just before collision is
`u=√(2gh)`

`u=√(2\time 9.8* 2.54)`

`u=7.05 m/s`

if the now if the ball rises to a height of 175 cm , velocity after collision to reach at that height is

`v_a=√(2* 9.8* 1.75)=5.85 m/s`

if the ball rises to an height of 185 cm then velocity after collision

`v_b=√(2* 9.8* 1.85)=6.02 m/s`

value of e for
`h=175 cm`

`e=(5.85)/(7.05)`

`e=0.829`

e for 185 cm

`e=(6.02)/(7.05)=0.853`

Range of e is 0.829 to 0.853