A ball A is falling vertically downwards with velocity v1. It strikes elastically with a wedge moving horizontally with velocity v2 as shown in figure. What must be the ratio so that the ball bounces back in vertically upwards direction relative to wedge?
In the figure v12 = velocity of ball w.r.t wedge before collision and v12 = velocity of ball w.r.t wedge after collision, which must be in vertically upward direction as shown. In elastic collision v12 and v12 will make equal angle (say) with the normal to the plane.
We can show that α = 30∘
∴∠MON = 30∘
Now v1v2 = tan 30∘ = 1√3