A boy in the elevator shoots a bullet in a vertical upward direction from a height of 1.5 m above the floor of the elevator. There is no roof in the elevator. The floor of the elevator is at 50 m from ground at the instant when velocity of the elevator is 10 m/s in upward direction. The bullet strikes the floor of the elevator in 2 seconds. The initial speed of the bullet is 15 m/s relative to the elevator.
Q. Find the acceleration of the elevator in upward direction, `((ms)/(s^2))`:

Options

A. 5
B. 5.25
C. 5.75
D. 6.25

Answer

A

Explanation

Subscript B stands for bullet, E for elevator, and G for ground.
`vecV_(BE)=15(m)/(s)` `(uarr)`
`veca_(BE)=veca_(BG)-veca_(EG)`
`=-g-(-a)=(g+1)(darr)`
in the frame of elevator (for bullet)
`s=ut+(1)/(2)a^2`
`-1.5=15t-(1)/(2)(g+a)t^2`given`t=2` sec
`-1.5=30-2(g+a)`
`veca=veca_(EG)=15.75-g=5.75(m)/(s^2)(uarr)`