A figure skater along a circular path of radius 5 m. If she coasts around one half of the circle, find (a) the magnitude of the displacement vector and (b) what distance she skated? (c) What is the magnitude of the displacement if she skates all the way around the circle?

- anonymous

- schrodinger

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- mathstudent55

Do you know what is the difference between the "magnitude of the displacement vector" and "the actual distance skated" (parts a and b)?

- anonymous

Magnitude of displacement is the straight line distance from the beginning of a path to the end of the path. What is the length of the straight line drawn from the beginning position to a point half way around the circle?

- mathstudent55

|dw:1438648778741:dw|

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## More answers

- anonymous

@mathstudent55 as far as I know, part b is half circumference of a circle (?) and a i don't know hehe

- mathstudent55

In other words, part a is the diameter of the circle, part b is the half-circumference of the circle.

- mathstudent55

For part c, she goes one full circle.
She ends up where she started, so the magnitude of the displacement vector is zero.
The distance is the circumference.

- anonymous

@ospreytriple the half part of a circle is 5 m therefore, 2r=10 (?)

- anonymous

Exactly. Good job.

- anonymous

@ospreytriple Thanks :)

- mathstudent55

Part a: diameter = 2r
Part b: half circumference = pi * r
Part c: magnitude = 0; distance = circumference = 2*pi*r

- anonymous

For the second question you need to calculate the actual length of the path. So it is half of the circumference of the circle. Can you calculate that?

- anonymous

@mathstudent55 Thanks :)

- anonymous

@ospreytriple I answered: 1/2 x 2 x pi x r therefore: 78.57 (?)

- mathstudent55

1/2 * 2 * pi * r = pi * r = 3.14 * 5 m
How do you get such a large number?

- anonymous

@mathstudent55 1/2 x 2 x 22/7 x 5 x 5 hehe I don't know (?)

- mathstudent55

The radius, r, is not squared for the circumference. It is only squared for the area.

- mathstudent55

|dw:1438649386383:dw|

- anonymous

@mathstudent55 okay thanks :) So the final answer is 15.7 (?)

- mathstudent55

|dw:1438649464150:dw|

- mathstudent55

Correct. That is the answer for part b.

- anonymous

@mathstudent55 Thank you so much ^_^

- mathstudent55

Then for part c you need to do the same two things you did for parts a and b, but now for a full circle.

- mathstudent55

|dw:1438649568860:dw|

- anonymous

I get it. So for part c the answer is zero (?)

- mathstudent55

The figure above is for part c.

- mathstudent55

Part c has two parts.
First, the magnitude of the distance vector is zero.
Then the second part of part c is the distance traveled. That is the full circumference, so take your answer before, 15.7 m (half a circumference), and multiply it by 2.

- anonymous

@mathstudent55 Thanks :)

- mathstudent55

You're welcome.

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