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

detailed solution

Correct option is B

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 =   (V sin α)2+(V​cos α)2 substitute equation (1) , (2) V =   (u sin θ)2+(eu​cos θ)2 ∴    V =   ue2cos2 θ+sin2 θ