Displacement and Velocity on a Circular Track

[Canada54211]

Homework Statement

[/B]
Student runs 3.4 laps in 30 minutes on a circular track with a radius 100m, She begins at the western most point of the track and travels clockwise. after this she gets sidetracked by the ice-cream truck, and follows it due west for twenty seconds at 4m/s.
a) determine her resultant displacement
b) determine her resultant velocity

I figured the circumference was 628.3m even though I'm not sure that helps me. I can't find out where 3.4 laps leaves her on the track.

 

[berkeman]

Homework Statement

[/B]
Student runs 3.4 laps in 30 minutes on a circular track with a radius 100m, She begins at the western most point of the track and travels clockwise. after this she gets sidetracked by the ice-cream truck, and follows it due west for twenty seconds at 4m/s.
a) determine her resultant displacement
b) determine her resultant velocity

I figured the circumference was 628.3m even though I'm not sure that helps me. I can't find out where 3.4 laps leaves her on the track.

Welcome to the PF.

One lap leaves her at her starting point, which is the westernmost point on the track (the left middle point on the track). 3 laps leaves her at the same point. There are 2π radians (360 degrees) in a circle. How much is 0.4 of a lap? Then draw a line from that point straight to the west (to the left) with a length determined by her speed 4m/s for 20 seconds. How long is that line? And where is the final point on that line compared to her starting point on the circle?

 

[drvrm]

Homework Statement

[/B]
Student runs 3.4 laps in 30 minutes on a circular track with a radius 100m, She begins at the western most point of the track and travels clockwise. after this she gets sidetracked by the ice-cream truck, and follows it due west for twenty seconds at 4m/s.
a) determine her resultant displacement
b) determine her resultant velocity

I figured the circumference was 628.3m even though I'm not sure that helps me. I can't find out where 3.4 laps leaves her on the track.

draw a circle of 100 meters on paper///then locate the runner after 3.4 laps starting from west and moving clock wise...so she must be near north towards east ..locate it
calculate its velocity /speed =3.4 laps/30 minutes .then draw the final velocity towards west and then calculate the resultant..

 

[Canada54211]

Welcome to the PF.

One lap leaves her at her starting point, which is the westernmost point on the track (the left middle point on the track). 3 laps leaves her at the same point. There are 2π radians (360 degrees) in a circle. How much is 0.4 of a lap? Then draw a line from that point straight to the west (to the left) with a length determined by her speed 4m/s for 20 seconds. How long is that line? And where is the final point on that line compared to her starting point on the circle?

So if 0.4 of a lap is 251.32m then where would that leave me on the circle? at 251 degrees or does it matter and I just plot it there?

 

[berkeman]

So if 0.4 of a lap is 251.32m then where would that leave me on the circle? at 251 degrees or does it matter and I just plot it there?

How is 0.4 * 360 degrees equal to 251 degrees?

 

[Canada54211]

How is 0.4 * 360 degrees equal to 251 degrees?

lol I am not sure I just can't figure out where that point would end up.
so its 144degrees off the starting point? so like N54E? or N144E if from Starting point

 

[berkeman]

lol I am not sure I just can't figure out where that point would end up.
so its 144degrees off the starting point? so like N54E? or N144E if from Starting point

I'm not sure of the standard way to express the point in N/E notiation, but it would be at the 144 degree mark on the outer scale of the figure below, that starts at 0 at the left, and progresses up to 180 degrees clockwise...

http://www.mathstips.com/wp-content/uploads/2014/01/measure-angle.png

 

[haruspex]

N54E

yes.

 

[Canada54211]

Ok thank you for the help