At a metro station, a girl walks up a stationary escalator in time. t _(1),If she remains stationary on the escalator, then the escalator take her up in time t_(2). The time taken by her to walk up on the moving escalator will be

At a metro station, a girl walks up a stationary escalator in time. t

1.	At a metro station, a girl walks up a stationary escalator in time. t _(1),If she remains stationary on the escalator, then the escalator take her up in time t_(2). The time taken by her to walk up on the moving escalator will be
Answer» `(t_(1) +t_(2)) //2` `t _(1) t _(2) // (t - t _(1))` `t _(1) t _(2) //(t_(2) + t _(1))` `t _(1) - t _(2)` Solution :Net velocity with respectto the Earth that will be equal to velocity of the girl plus velocity of esaclator. Let displacemtn is L, then velocity of girl `v _(g) = (L)/(t _(1)) ` velocity of escaltoor `v _(e) = (L)/(t _(2))` Net velocity of the girl, `v =v _(g) + v _(e) = (L)/(t_(1)) + (L)/(t_(2)) ...(i)` If t is total time taken in covering distance L, then `v = L/t` Using in (i) `L/t = (L)/(t _(1)) + (L)/(t _(2)) IMPLIES t = (t_(1) t_(2))/(t _(1) + t _(2))`