A ball A is falling vertically downwards with velocity v_(r) 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 ballbounces back in vertically upward direction relative to the wedge

A ball A is falling vertically downwards with velocity v_(r) It strike

1.	A ball A is falling vertically downwards with velocity v_(r) 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 ballbounces back in vertically upward direction relative to the wedge
Answer» SOLUTION :In the FIGURE `BAR(v_(12))` = velocity of ball w.r.t wedge before collision and `bar(v_(12)^(1))` = velocity of ball w.r.t wedge after collision, which must be in VERTICALLY upward direction as shwon. In elastic collision, `bar(v_(12))andbar(v_(12)^(1))` will MAKE equal angles `("say" alpha)` with the normal to the plane. We can show that `alpha = 30^(@)`, `therefore angleMON = 30^(@)` Now `(v_(1))/(v_(2)) = tan 30^(@) = (1)/(sqrt(3))`