A ball falls freely from rest on to a hard horizontal floor and repeatedly bounces. If the velocity of the ball just before the first bounce is 7 ~ms ⁻¹ and the coefficient of restitution is 0.75 . The total distance travelled by the ball before it comes to rest is (acceleration due to gravity =10 ~ms ⁻² )

Step-by-step solution

l =0.75, u =7 ~ms ⁻¹ Total distance traveled, S = H +2 H ₁+2 H ₂+ aligned & = u^2 2 g +2 (e u)^2 2 g +2 (e^2 u )^2 2 g + .+ & = u^2 2 g (1+2 e^2+2 e^4+ . .+ ) & = u^2 2 g + e^2 u^2 g (1+e^2+e^4+ + ) & = u^2 2 g + e^2 u^2 g ( 1 1-e^2 )= u^2 g ( 1 2 + e^2 1-e^2 ) & = u^2 2 g ( 1+e^2 1-e^2 )= 7 7 2 10 [ 1+(0.75)^2 1-(0.75)^2 ] aligned