A ball falls freely on a perfectly elastic plate from a height of 3m . At the instant t = 0 , the velocity of the ball is zero. Draw velocity -time graph for the motion of the ball. [g = 9.8 `"m.s"^(-2)` ]

Explanation

In this case h `= (1)/(2) "gt"^(2)`
The time taken by the ball in falling through 3 m is given by
`t = sqrt((2h)/(g))=sqrt((2xx3)/(9.8)) =0.793`s
According to the equation `v^(2)` = 2gh, the velocity of the ball just before striking the plate is given by
`v = (sqrt(2gh)=sqrt(2xx9.8 xx3.0)=7.67 "m.s"^(-1)`

Since the plate is perfectly elastic the ball after striking it will rebound with the same velocity `(7.67 "m.s"^(-1))` and its velocity will become zero after the same time (0.78). This motion will be repeated again and again as shown in the above graph.