JEE MAIN - Physics (2021 - 20th July Evening Shift - No. 2)
A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a moving escalator then the escalator takes him up in time t2. The time taken by him to walk up on the moving escalator will be :
$${{{t_1}{t_2}} \over {{t_2} - {t_1}}}$$
$${{{t_1} + {t_2}} \over 2}$$
$${{{t_1}{t_2}} \over {{t_2} + {t_1}}}$$
$${t_2} - {t_1}$$
Explanation
L = Length of escalator
$${V_{b/esc}} = {L \over {{t_1}}}$$
When only escalator is moving.
$${V_{esc}} = {L \over {{t_2}}}$$
when both are moving
$${V_{b/g}} = {V_{b/esc}} + {V_{esc}}$$
$${V_{b/g}} = {L \over {{t_1}}} + {L \over {{t_2}}} \Rightarrow \left[ {t = {L \over {{V_{b/g}}}} = {{{t_1}{t_2}} \over {{t_1} + {t_2}}}} \right]$$
$${V_{b/esc}} = {L \over {{t_1}}}$$
When only escalator is moving.
$${V_{esc}} = {L \over {{t_2}}}$$
when both are moving
$${V_{b/g}} = {V_{b/esc}} + {V_{esc}}$$
$${V_{b/g}} = {L \over {{t_1}}} + {L \over {{t_2}}} \Rightarrow \left[ {t = {L \over {{V_{b/g}}}} = {{{t_1}{t_2}} \over {{t_1} + {t_2}}}} \right]$$
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