A body is thrown up in a lift with a velocity u relative to the lift and the time of flight is t. Show that the lift is moving up with an acceleration $\frac{2 u - t g}{t} .$

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Solution

Let the acceleration of the lift be $a$ in upward direction.
Acceleration of the body w.r.t ground $= g$ (downward)
Thus Acceleration of the body w.r.t lift $a_{b} = g + a$
In the lift frame : $S = u t + \frac{1}{2} a_{b} t^{2}$ where $t$ is the time of flight
$∴$ $0 = u t - \frac{(g + a) t^{2}}{2}$ $⟹ a = \frac{2 u - t g}{t}$

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A body is thrown up in a lift with a velocity u relative to the lift and the time of flight is t. Show that the lift is moving up with an acceleration 2u−tgt.

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A body is thrown up in a lift with a velocity u relative to the lift and the time of flight is t. Show that the lift is moving up with an acceleration $\frac{2 u - t g}{t} .$