First slide

Relative velocity in 1-d

Question

It takes one minute for a passenger standing on an escalator to reach the top. If the escalator does not move it takes him 3 minute to walk up. How long will it take for the passenger to arrive at the top if he walks up the moving escalator?

Moderate

A

30 sec
B

45 sec
C

40 sec
D

35 sec

Solution

$Let speed of elevator is v_{e}$
$t_{1} = \frac{L}{v_{e}} \Rightarrow 1 \min = \frac{L}{v_{e}}$
$Let speed of person relative to elevator is v_{P} then$
$t_{2} = \frac{L}{v_{p}} \Rightarrow 3 min = \frac{L}{v_{p}}$
$when the escalator is moving:$
$t_{3} = \frac{L}{v_{e} + v_{p}} = \frac{L}{\frac{L}{1 min} + \frac{L}{3 min}} = \frac{3}{4} min = 45 s$

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