- #1

UMich1344

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## 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?

## Homework Equations

Addition/subtraction of relative velocities.

## The Attempt at a Solution

The velocity of the

**S**tudent relative to the

**G**round 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.

**[tex]\vec{v}[/tex]**

_{SG}= velocity of the

**S**tudent relative to the

**G**round = [tex]\frac{x}{t}[/tex] = [tex]\frac{+30.0}{11}[/tex] = +2.727272727 m/s

**[tex]\vec{v}[/tex]**

_{SE}= velocity of the

**S**tudent relative to the

**E**scalator

**[tex]\vec{v}[/tex]**

_{EG}= velocity of the

**E**scalator relative to the

**G**round = +1.8 m/s

**[tex]\vec{v}[/tex]**

_{SG}=

**[tex]\vec{v}[/tex]**

_{SE}+

**[tex]\vec{v}[/tex]**

_{EG}

**[tex]\vec{v}[/tex]**

_{SE}=

**[tex]\vec{v}[/tex]**

_{SG}-

**[tex]\vec{v}[/tex]**

_{EG}

**[tex]\vec{v}[/tex]**

_{SE}= (+2.727272727 m/s) - (+1.8 m/s)

**[tex]\vec{v}[/tex]**

_{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.