Finding Displacement of Elevator in Accelerating Frame

[erisedk]

Homework Statement

A boy standing in an elevator accelerating upward throws a ball upward with a v_o.
The ball returns to his hands after time t. The acceleration of the lift is

Homework Equations

The Attempt at a Solution

After time t, displacement of the ball = displacement of the lift
v_o t - 1/2 gt² = ?
What should the displacement of the lift be?
According to me, it should be ut + 1/2at².
Problem is, I don't know what the initial velocity of the lift is, i.e. what u is.
What do I do?

 

[TSny]

The quantity v₀ is probably to be interpreted as the initial velocity of the ball relative to the elevator. You are writing equations relative to the ground. So, what is the initial velocity of the ball relative to the ground?

 

[Orodruin]

You are likely expected to understand that the velocity v0 is the velocity of the ball relative to the elevator. You can make any assumption on the velocity of the elevator, it should not affect the result - simply assume it is an undetermined velocity u.

 

[erisedk]

Ok thank you!
So, displacement of the body in the frame of the elevator is 0 in time t, and so I can consider a pseudo force a on the elevator.
v0t - 1/2 (g+a) t^2 = 0
a= (2v0 - gt)/t

 

[Orodruin]

Correct.