A platform of infinite mass is moving upward with velocity `5 m//s`. At time `t = 0`, a ball which is at height `100 m` above the platform starts fallng freely. If the velocity of ball just after the collision is `10 v m//s` then value of v is (Assum elastic collision) `(g = 10 m//s^(2))`:

Answer

5

Explanation

`x = (1)/(2) g t^(2)` .....(1) (for ball)
`100 - x 5t` .....(2) for (plat form)
From (1) & (2), we get
`100 - (1)/(2) g t^(2) = 5t`
`100 - 5 t^(2) = 5t`
`t^(2) + t - 20 = 0`
`(t - 4) (t + 5) = 0`
`t = 4s`
Velocity of ball after `4s`,
`v' = 0 + 10 xx 4 = 40 m//s`
Velocity of ball just after collision
`v'' = (40 - (- 5)) + 5`
`v'' = 50 m//s = 10 v rArr v = 5`