First slide
Collisions
Question

A particle strikes a horizontal friction less floor with a speed u, at an angle  θ,  with the vertical and rebounds with a speed V, at an angle α with vertical .  Find the value of V if e is the coefficient of restitution.

Moderate
Solution

 

resolve u into components as , vertical component ucosθ=u1,horizontal component usinθ resolve v into components as , vertical component vcosα=v1,horizontal component vsinα  coefficient of restitution e=v2-v1u1-u2 here v2=u2=0 =velocity of the floor substitute given values in e e=0-vcosαucosθ-0 -vcosα=eucosθ---(1) horizontal components are not changed   usinθ=vsinα---(2) V=   (Vsinα)2+(Vcosα)2 substitute equation (1) , (2) V=   (usinθ)2+(eucosθ)2     V=   ue2cos2θ+sin2θ

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