Question

An escalator is 18.3 m long. If a person stands on the escalator, it takes 47.8 s to ride from the bottom to the top. If a person walks up the moving escalator with a speed of 0.521 m/s relative to the escalator, how long does it take the person to get to the top?

Answer 1

Answer:

20.243 s

Explanation:

Because the escalator and person moving in the same direction, relative velocity can be calculated by summing the velocity of the escalator and velocity of the person.  

The speed of escalator can be calculated as,

$v_{escalator}=\frac{x}{t}=\frac{18.3}{47.8}=0.383\ m/s$

Relative velocity

$v_{relative}=v_{escalator}+v_{person}\\\\v_{relative}=0.383+0.521=0.904\ m/s$

Therefore total time required to take the person to get to the top

$t=\frac{x}{v_{relative}}= \frac{18.3}{0.904}=20.243\ s$