A block $A$ can slide on a frictionless incline of angle $θ$ and length $l$ , kept inside an elevator going up with uniform velocity $v$ . Find the time taken by the block to slide shown the length of the incline if it is released from the top of the incline.

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Solution

Since, the elevator is moving with a uniform velocity its acceleration is zero. let the block move on the incline. The forces on the block are the gravitational force and the normal force. therefore the equation of motion of the along the incline is

$\begin{matrix} m g sin θ = m a \Rightarrow a = g s i n θ \end{matrix}$
which is constant,
therefore from the motion of block

$\begin{matrix} l = u t + \frac{1}{2} a t^{2} = \frac{1}{2} a t^{2} \Rightarrow t = \sqrt{\frac{2 l}{a}} = \sqrt{\frac{2 l}{g sin θ}} \end{matrix}$

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