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Relative Velocity

A person walk...

Question

A person walks up a stationary escalator in $t_{1}$ second. If he remains stationary on the escalator, then it can take him up in $t_{2}$ second. If the length of the escalator is L, then how much time would it take him to walk up the moving escalator?

A

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B

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C

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D

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Solution

The correct option is B

Speed of man w.r.t. the ground $v_{m} = v_{m c} + v_{c} \Rightarrow v_{m} = \frac{L}{t_{1}} + \frac{L}{t_{2}} = L [\frac{1}{t_{1}} + \frac{1}{t_{2}}] + L [\frac{t_{1} + t_{2}}{t_{1} t_{2}}]$

$\Rightarrow t = \frac{L}{v_{m}} = [\frac{t_{1} t_{2}}{t_{1} + t_{2}}]$ the time taken by the man to walk up the moving escalator.

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