Displacement and Velocity on a Circular Track

In summary, the student runs 3.4 laps in 30 minutes on a circular track with a radius of 100m, starting at the westernmost point and moving clockwise. After running, she gets sidetracked by an ice-cream truck and follows it due west for 20 seconds at a speed of 4m/s. Her resultant displacement is at the N54E point on the outer scale of the figure, which starts at 0 at the left and progresses up to 180 degrees clockwise. Her resultant velocity can be calculated as 3.4 laps/30 minutes.
  • #1
Canada54211
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0

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.
 
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  • #2
Canada54211 said:

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. :smile:

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? :smile:
 
  • #3
Canada54211 said:

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..
 
  • #4
berkeman said:
Welcome to the PF. :smile:

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? :smile:
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?
 
  • #5
Canada54211 said:
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? :smile:
 
  • #6
berkeman said:
How is 0.4 * 360 degrees equal to 251 degrees? :smile:
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
 
  • #7
Canada54211 said:
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
measure-angle.png
 

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  • #8
Canada54211 said:
N54E
yes.
 
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Likes berkeman
  • #9
Ok thank you for the help
 

Related to Displacement and Velocity on a Circular Track

1. What is circular track displacement?

Circular track displacement is a scientific concept that describes the distance and direction an object travels along a circular track.

2. How is circular track displacement calculated?

Circular track displacement is calculated using the formula d = 2πr, where d is the displacement, π is the mathematical constant pi, and r is the radius of the circular track.

3. What is the difference between circular track displacement and linear displacement?

Circular track displacement is a type of displacement that occurs when an object travels along a circular path, while linear displacement refers to the distance an object travels in a straight line from its starting point to its ending point.

4. How does the speed of an object affect its circular track displacement?

The speed of an object affects its circular track displacement by determining how far and how quickly the object will travel along the circular path. The faster the object moves, the greater its displacement will be.

5. Can circular track displacement be negative?

Yes, circular track displacement can be negative if the object travels in the opposite direction of its starting point. In this case, the negative sign indicates that the object has moved in the opposite direction of its starting point.

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