# Relative Velocity of an escalator

• UMich1344
In summary, the conversation discusses the calculation of the speed a student must exceed in order to beat the local record time of 11 seconds for running in the wrong direction on an escalator with a length of 30.0 m and a speed of 1.8 m/s. The equation used is the addition/subtraction of relative velocities. The calculated speed is 0.93 m/s. The student must exceed this speed in order to beat the record.
UMich1344

## Homework Statement

The escalator that leads down into a subway station has a length of 30.0 m and a speed of 1.8 m/s relative to the ground. A student is coming out of the station by running in the wrong direction on this escalator. The local record time for this trick is 11 s. Relative to the escalator, what speed must the student exceed in order to beat the record?

## The Attempt at a Solution

The velocity of the Student relative to the Ground is equal to the length of the escalator divided by the time it takes to travel the length of the escalator. In this scenario, the time will be the local record time as given.

We know from the given information that x = +30.0 m and t = 11 s.

$$\vec{v}$$SG = velocity of the Student relative to the Ground = $$\frac{x}{t}$$ = $$\frac{+30.0}{11}$$ = +2.727272727 m/s
$$\vec{v}$$SE = velocity of the Student relative to the Escalator
$$\vec{v}$$EG = velocity of the Escalator relative to the Ground = +1.8 m/s

$$\vec{v}$$SG = $$\vec{v}$$SE + $$\vec{v}$$EG

$$\vec{v}$$SE = $$\vec{v}$$SG - $$\vec{v}$$EG
$$\vec{v}$$SE = (+2.727272727 m/s) - (+1.8 m/s)
$$\vec{v}$$SE = 0.92727273 m/s

Relative to the escalator, the student must exceed a speed of 0.93 m/s [to the correct number of significant figures (2)].

Question

I feel pretty confident that I've approached this one the right way. Could someone please take the time to look it over and give me some feedback? Thank you... I really appreciate it.

That looks ok.

Your solution appears to be correct. You have correctly used the formula for relative velocity and have accounted for the direction of movement in your calculations. Your answer is also given to the correct number of significant figures. Great job!

## What is relative velocity of an escalator?

The relative velocity of an escalator is the difference between the velocity of a person walking on the escalator and the velocity of the escalator itself.

## How is relative velocity of an escalator calculated?

The relative velocity of an escalator can be calculated by subtracting the velocity of the escalator from the velocity of the person walking on the escalator.

## Why is relative velocity of an escalator important?

Relative velocity of an escalator is important in understanding the motion of a person walking on an escalator and how it differs from walking on a stationary surface. It can also help in analyzing the efficiency of the escalator and its impact on the person's movement.

## Does the relative velocity of an escalator change with the direction of movement?

Yes, the relative velocity of an escalator changes with the direction of movement. When a person is walking in the same direction as the escalator, the relative velocity is the sum of their individual velocities. However, when a person walks in the opposite direction, the relative velocity is the difference between their velocities.

## How does the angle of the escalator affect the relative velocity?

The angle of the escalator does not affect the relative velocity. The relative velocity is only dependent on the difference between the velocities of the person and the escalator, not on the angle of the escalator.

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