A particle slides down a smooth inclined plane of elevation `theta` fixed in an elevator going up with an acceleration `a_0`. The base of the incline has a length L. Find the time taken by the particle to reach the bottom.

Explanation

Let us wormk in the elevator frame. A pseudo force `m_0` n the downward direction is to be applied on the particle of mass m are.
i. N normal force
ii. mg downward (by the earth),
iii. `ma_0` downward (pseudo)
Let a be the acceleration of eth partice withrespect to the incline. Taking components of the forces paralel to the incline and applying Newton's law,
`mg sintheta +ma_0 sin theta =m a
or ` a=(g+a_0) sin theta`
This is the acceleration with respect t the elevator. In this frame the distnce traveled by the particle is `L/costheta.` Hence,
`L/costheta=1/2(g+a_0) sin theta.t^2,
or, `t=[(2L)/((g+a_0)sinthetacostheta)]^(1/2)]`