Solving Escalator Motion Problems: A Shopper's Guide

[sultaN-PL]

I really do not understand this question...what kind of formula can I use, because there is no displacement/distance? any help? What do I do since there is only one variable? thanks in advance.

QUESTION: A shopper can ride up a moving escalator in 15 s. When the escalator is turned off, the shopper can walk up the stationary escalator in 8 s. a) How long would it take the shopper to walk up the moving escalator? b) Could the shopper walk down the moving escalator to the floor below? if so how long would it take?

 

[Andrew Mason]

I really do not understand this question...what kind of formula can I use, because there is no displacement/distance? any help? What do I do since there is only one variable? thanks in advance.

QUESTION: A shopper can ride up a moving escalator in 15 s. When the escalator is turned off, the shopper can walk up the stationary escalator in 8 s. a) How long would it take the shopper to walk up the moving escalator? b) Could the shopper walk down the moving escalator to the floor below? if so how long would it take?

The speed of the escalator is +L/15 m/sec where L is the length in metres. Her speed relative to the escaltor is + or - L/8 (m/sec). Her speed relative to the ground is _____? The distance is L. So how long does that take?

AM

 

[kyle8921]

I would suggest using the formula v=d/t, where v is the velocity, d is the displacement or distance, and t is the time. In this case, the variable of interest is time, which we can solve for using the given information.

a) To find the time it would take the shopper to walk up the moving escalator, we can set up the equation:

15 s = (d/t) + 8 s

Where d is the distance of the escalator. Since we do not know the distance, we can use the fact that the shopper is walking at the same speed in both scenarios, so the distance walked should be the same. Therefore, we can set the distances equal to each other and solve for t:

15 s = (8 s + d)/t

15t = 8s + d

d = 15t - 8s

Now we can substitute this value for d into our original equation and solve for t:

15 s = (15t - 8s)/t

15t = 15t - 8s

8s = 0

s = 0

Therefore, it would take the shopper 0 seconds to walk up the moving escalator, as they are already on it and not walking.

b) Yes, the shopper could walk down the moving escalator to the floor below. To find the time it would take, we can use the same formula as before, but with the shopper walking in the opposite direction:

15 s = (d/t) - 8 s

Solving for t:

15 s = (8 s - d)/t

15t = 8s - d

d = 8s - 15t

Substituting this value for d into the original equation and solving for t:

15 s = (8s - 15t)/t

15t = 8s - 15t

30t = 8s

t = 8s/30

t = 4/15 s

Therefore, it would take the shopper 4/15 seconds to walk down the moving escalator.

I hope this helps to clarify the problem and provide a solution using a scientific approach. If you have further questions or need additional help, please don't hesitate to ask.