A ball collides with a fixed inclined plane of inclination θ after falling through a distance h . If it moves horizontally just after the impact the coefficient of restitution is

Writing coefficient of restitution equatione=v2−v1u1−u2 initial velocity be v0; resolve into components, as v0cosθ perpendicular to the plane downward=u1                                       and v0sinθ parallel to the plane downward final velocity be v;resolve into components, as vcosθ parallel to the plane                                        and vsinθ perpendicular to the plane upward=v1 substitute legibly e=0−vsinθ−v0cosθ−0 e=vv0tanθ---(1)The velocity of ball will remain unchanged in the direction of sloping surface (common tangent)V0 sin θ = v cos θ⇒vv0=tanθ---(2)substitute eqn(2) in eqn(1)⇒e=tan2θ