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A ball A is falling vertically downwards...

A ball A is falling vertically downwards with velocity `v_(1)` . It strikes elastically with a wedge moving horizontally with velocity `v_(2)` as shown in figure . What must be the ratio `(v_(1))/(v_(2))` , so that the ball bounces back in vertically upward direction relative to the wedge

Text Solution

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In the figure `vec(v_(12))` = velocity of ball w.r.t. wedge before collision and `vec(v)_(12)^(1)=` velocity of ball w.r.t. wedge after collision, which must be in vertically upward direction as shown.

In elastic collision, `vec(v_(12))` and `vec(v_(12)^(1))` will make equal angles (say `alpha`) with the normal to the plane. We can show that `alpha = 30^(@)`,
`therefore angle MON = 30^(@)` Now `(v_(1))/(v_(2))=tan 30^(@)=(1)/(sqrt(3))`
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