An inelastic ball is projected with velocity $v_{0} = \sqrt{g h}$ , at an angle $α$ to the horizontal, towards a wall at a distance d from the point of projection. After collision the ball returns to the point of projection. What is the coefficient of restitution between ball and wall ( $α = 45^{0}$ )

Question

Infinity Learn · Accepted Answer

Time taken to return to the point of projection after  impact  $$=dev0cos$$α Total time of flight $$=dv0cos$$α$$+dev0cos$$α$$=dghcos$$α[$$1+ee$$]There is no change in the vertical component of the velocity after impact, therefore total time offlight remains unchanged.$$T=2v0sin$$α$$g=2ghsin$$αgdghcosα(1+ee)=2ghsin$$αgOr  $$(1+ee)=hsin2$$αdOr $$e=d(hsin2$$α−$$d)

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An inelastic ball is projected with velocity v0=gh , at an angle α to the horizontal, towards a wall at a distance d from the point of projection. After collision the ball returns to the point of projection. What is the coefficient of restitution between ball and wall ( α=450 )

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