PYQ NEET- Motion In A Straight Line Kinematics L-4

Question: Preeti reached the metro station and found that the escalator was not working. She walked up the sationary escalator in time $t_1$. On another days, if she remains stationary on the moving escalator, then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be#

A) $\frac{t_1 t_2}{t_2-t_1}$

B) $\frac{t_1 t_2}{t_2+t_1}$

C) $t_1-t_2$

D) $\frac{t_1+t_2}{2}$

Answer: $\frac{t_1 t_2}{t_2+t_1}$#

Sol:#

Velocity of preeti with respect to elevator $\mathrm{v}_1=\frac{d}{t_1}$ Velocity of elevator with respect to ground $\mathrm{v}_2=\frac{d}{t_2}$ $\therefore$ Net velocity of preeti on moving escalator with respect to the ground $$ \begin{aligned} & \mathrm{v}=\mathrm{v}_1+\mathrm{v}_2 \ & \frac{d}{t}=\frac{d}{t_1}+\frac{d}{t_2} \ & \frac{1}{t}=\frac{1}{t_1}+\frac{1}{t_2} \ & \therefore \mathrm{t}=\frac{t_1 t_2}{t_1+t_2} \end{aligned} $$

Here $t$ is the time taken by preeti to walk up on the moving escalator.