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Velocity in 2D

Preeti reache...

Question

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_{1}$ . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_{2}$ . The time taken by her walk up on the moving escalator will be

A

t_{1} - t_{2}

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B

\frac{t_{1} + t_{2}}{2}

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C

\frac{t_{1} t_{2}}{t_{2} - t_{1}}

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D

\frac{t_{1} t_{2}}{t_{1} + t_{2}}

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Solution

The correct option is D $\frac{t_{1} t_{2}}{t_{1} + t_{2}}$
$t_{1} =$ time taken at stationary escalator
$t_{2} =$ time taken at moving escalator
$t^{'} =$ time taken in walking up the moving escalator
$d =$ displacement of escalator
$V_{1} =$ Velocity of Preeti
$V_{2} =$ Velocity of escalator
$(V_{1} + V_{2}) = \frac{d}{t^{'}}$ , as $V_{1} = \frac{d}{t_{1}}, V_{2} = \frac{d}{t_{2}}$
$\frac{d}{t_{1}} + \frac{d}{t_{2}} = \frac{d}{t^{'}} \Rightarrow t^{'} = \frac{t_{1} t_{2}}{t_{1} + t_{2}}$

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