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`)
1. The time in which the ball strikes the floor of elevator is given by

Options

A. 2.13 s
B. 4.26 s
C. 1.0 s
D. 2.0 s

Answer

A

Explanation

a. Initial velocity of ball w.r.t ground.
`vecv_(BG) = vecv_(BE) + vecv_(EG) = 15 + 10 = 25ms^(-1) uparrow`
`vecv_(BE) = 15ms^(-1) uparrow, veca_(BG) = 10ms^(-2)downarrow`
`veca(BE) = veca_(BG) - veca_(EG) = 10- (-5) = 15 ms^(-2) downarrow`
`vecs_(BE) = 2m downarrow. Using s= ut + 1/2 at^2`
w.r.t. elevator frame,
`- 2 = 15 t - 1/2 xx 15^2 rArr t = 2.13s`
.