A boy reaches the airport and finds that the escalator is not...

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

Options

A $\dfrac{{t}_{1}{t}_{2}}{{t}_{2} - {t}_{1}}$
B $\dfrac{{t}_{1} + {t}_{2}}{2}$
C $\dfrac{{t}_{1}{t}_{2}}{{t}_{2} + {t}_{1}}$
D ${t}_{2} - {t}_{1}$

Correct answer

C. $\dfrac{{t}_{1}{t}_{2}}{{t}_{2} + {t}_{1}}$

Step-by-step solution

$L =$ Length of escalator

${V}_{b / ecc} = \dfrac{L}{{t}_{1}}$

When only escalator is moving,

${V}_{esc} = \dfrac{L}{{t}_{2}}$

when both are moving,

${V}_{b / g} = {V}_{b / esc} + {V}_{esc}$

${V}_{b / g} = \dfrac{L}{{t}_{1}} + \dfrac{L}{{t}_{2}} ⇒ \left[t = \dfrac{L}{{V}_{b / g}} = \dfrac{{t}_{1}{t}_{2}}{{t}_{1} + {t}_{2}}\right]$

Practice Motion in Two Dimensions on Quantrex Academy →

More from Motion in Two Dimensions

A particle is thrown with a speed v from a point O at an angle θ with the horizontal… JEE Advanced 2026 A car moving with a speed of 54 km/h takes a turn of radius 20 m. A simple pendulum is… JEE Main 2026 Two identical bodies, projected with the same speed at two different angles cover the… JEE Main 2026 If x and y coordinates of a projectile as a function of time (t) are given as 24t and… JEE Main 2026 A gun mounted on the ground fires bullets in all directions with same speed. The farthest… JEE Main 2026 Two projectiles are projected with the same initial velocities at the 15^∘ and 30^∘ with… JEE Main 2026 A boy throws a ball into air at 45^ ∘ from the horizontal to land it on a roof of a… JEE Main 2026 An object is projected with kinetic energy K from a point A at an angle 60^ ∘ with the… JEE Main 2026 Full Motion in Two Dimensions list All JEE Main PYQs