Kinematics

JEE Main level, single correct, medium

189 of 308

Question 189 of 308

A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1.{t}_{1}. If he remains stationary on a moving escalator then the escalator takes him up in time t2.{t}_{2}. The time taken by him to walk up on the moving escalator will be:

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Answer: (C) t1t2t2+t1\dfrac{{t}_{1}{t}_{2}}{{t}_{2}+{t}_{1}}

L=L= Length of escalator
Vb/ecc=Lt1{V}_{b/ecc}=\dfrac{L}{{t}_{1}}
When only escalator is moving,
Vesc=Lt2{V}_{esc}=\dfrac{L}{{t}_{2}}
when both are moving,
Vb/g=Vb/esc+Vesc{V}_{b/g}={V}_{b/esc}+{V}_{esc}
Vb/g=Lt1+Lt2⇒[t=LVb/g=t1t2t1+t2]{V}_{b/g}=\dfrac{L}{{t}_{1}}+\dfrac{L}{{t}_{2}}\Rightarrow \left[t=\dfrac{L}{{V}_{b/g}}=\dfrac{{t}_{1}{t}_{2}}{{t}_{1}+{t}_{2}}\right]

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