A particle strikes a horizontal smooth floor with a velocity u making an angle θ with the floor and rebounds with velocity v making an angle ϕ with the floor. The coefficient of restitution between the particle and the floor is e.

Question

A  particle strikes a horizontal smooth floor with a velocity u making an angle θ      with the floor and  rebounds with velocity v making an angle ϕ      with the floor. The  coefficient of restitution between the particle and the floor is e.

Infinity Learn · Accepted Answer

vsinϕ$$=eusin$$θ$$----(1)$$ vcosϕ$$=ucos$$θ$$----(2)$$ (1) $$/(2)$$ $$tan$$ϕ$$=etan$$θ squaring and adding (1) and (2) we get $$v2(sin2$$ϕ$$+cos2$$ϕ$$)=e2u2sin2$$θ$$+u2cos2$$θ $$v2=e2u2sin2$$θ$$+u21-sin2$$θ $$v2=u2e2sin2$$θ$$+1-sin2$$θ $$v=u1-1-e2sin2$$θ $$v2(sin2$$ϕ$$+cos2$$ϕ$$)=e2u2sin2$$θ$$+u2cos2$$θ $$v2=u2e2sin2$$θ$$+cos2$$θ $$v2u2=e2sin2$$θ$$+cos2$$θ $$12mv212mu2=e2sin2$$θ$$+cos2$$θ $$KfKi=e2sin2$$θ$$+cos2$$θImpulse on the ball $$=$$ mvsinϕ$$+musin$$θ$$=$$ musinθ(e+1)    (e(usin$$θ$$)=vsin$$ϕ $$)

A particle strikes a horizontal smooth floor with a velocity u making an angle $θ$ with the floor and rebounds with velocity v making an angle $ϕ$ with the floor. The coefficient of restitution between the particle and the floor is e.

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