Question

An escalator is 15 m long. If a person stands on the escalator, it takes 50 s to ride to the top.
(a) If a person walks up the moving escalator with a speed of 0.600 m/s relative to the escalator, how long does it take the person to get to the top?

(b) If a person walks down the "up" escalator with the same relative speed as in part (a), how long does it take to reach the bottom?

Answer 1

From the condition, find the velocity of the escalator:

$$v=15/50=0.3\text{ m/s}.$$

(a) In this case, person's velocity adds to the escalator's one, so it will take a shorter time:

$$t_a=\frac{l_\text{escalator}}{v_\text{escalator}+v_\text{person}}, \\\space\\ t_a=15/(0.3+0.6)=16.7\text{ s}.$$

(b) In this case, use a similar equation:

$$t_b=\frac{l_\text{perso}}{v_\text{person}-v_\text{escalator}}, \\\space\\ t_b=15/(0.6-0.3)=50\text{ s}.$$