A particle slides down a smooth inclined plane of elevation $θ$ , fixed in an elevator going up with an acceleration $a_{0}$ (figure). The base of the incline has a length $L$ . Find the time taken by the particle to reach the bottom.

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Solution

$s = u t + \frac{1}{2} a t^{2} \frac{l}{c o s θ} = 0 + \frac{1}{2} (g s i n θ t^{2} + a s i n θ t^{2}) ∴ t = \sqrt{\frac{2 l}{c o s θ s i n θ (g + a)}}$

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A particle slides down a smooth inclined plane of elevation θ, fixed in an elevator going up with an acceleration a0 (figure). The base of the incline has a length L. Find the time taken by the particle to reach the bottom.

s=ut+12at2lcosθ=0+12(gsinθt2+asinθt2)∴t=√2lcosθsinθ(g+a)

A particle slides down a smooth inclined plane of elevation $θ$ , fixed in an elevator going up with an acceleration $a_{0}$ (figure). The base of the incline has a length $L$ . Find the time taken by the particle to reach the bottom.

$s = u t + \frac{1}{2} a t^{2} \frac{l}{c o s θ} = 0 + \frac{1}{2} (g s i n θ t^{2} + a s i n θ t^{2}) ∴ t = \sqrt{\frac{2 l}{c o s θ s i n θ (g + a)}}$