1. The problem statement, all variables and given/known data A smooth sphere falls vertically and strikes a fixed smooth plane inclined at an angle of ∅ to the horizontal.If the coefficient of restitution is (2/3) and the sphere rebounds horizontally, Its speed before impact is u and after impact v calculate the fraction of kinetic energy lost during impact. 2. Relevant equations 3. The attempt at a solution Diagram of the question is attached to this post. i = horizontal component vector and j = vertical component vector Taking the inclined plane as the x axis v, vcos∅i + vsin∅j ..... alternate angle to inclined angle u, vcos(90 - ∅ )i - v sin(90 - ∅)j = usin∅i - ucos∅j the I component remains the same vcos∅ = usin∅ v = utan∅ vsin∅/(ucos∅) = 2/3 (v/u)tan∅ = 2/3 (utan∅/u)tan∅ =2/3 (tan∅)^2 = 2/3 tan∅ = (√6)/3 v = u(√6)/3 .5mu^2 - .5mv^2 = energy loss .5mu^2 -.5m(6/9)u^2 = .5mu^2 - m(6/18)u^2 = .5mu^2 - (1/3)mu^2 = (1/6)mu^2 fraction of kinetic energy lost is 1/6 my book says the answer is 1/3 but I got 1/6. Any help would be appreciated.