An elevator without a ceiling is ascending up with an acceleration of `5 ms^-2.` A boy on the elevator shoots a ball in vertical upward direction from a height of 2 m above the floor of elevator. At this instant the elevator is moving up with a velocity of `10 ms^-1` and floor of the elevator is at a height of 50 m from the ground. The initial speed of the ball is `15 ms^-1` with respect to the elevator. Consider the duration for which the ball strikes the floor of elevator in answering following questions. (`g=10 ms^-2`)
4. The maximum separation between the floor of elevator and the ball during its flight would be

Options

A. 30 m
B. 15 m
C. 7.5 m
D. 9.5 m

Answer

D

Explanation

d. Displacement of ball w.r.t. elevator is given by
`s = 15t - 1/2 xx 15t^2`
Here s+2 will be separation between the floor of elevator and
ball.
For s to be maximum, `(ds)/(dt) = 0`
which gives t = 1 s
So maximum value of separation is
`(15 xx 1 - 1/2 xx 15 xx (1)^2) + 2 = 9.5 m ` .