Calculating Vectors: Displacement, Radius & Skating Distance

[tnhoots]

Homework Statement

1)A skater glides along a circular path of radius 4.90m.
a)if he coasta around one half of the circle, find the magnitude of the displacement vector
b)find how far the person skated
c)What is the magnitude of displacement if he skates all the way around the circle

Homework Equations

Area of a circle = pi(radius squared)

The Attempt at a Solution

-My first inclination for part a was to find the area of the circle and then multiply that by the degrees of one half the circle (180) and then do the same for c but multiply by (360). I am unsure of b. Is that the right path.

 

[Kurdt]

You are not really on the right lines. What is the definition of displacement? For part b you need to find the distance the person has skated. Since they skated half the circumference of a circle this should be easy to find.

 

[tnhoots]

part c

I found the solution to these problem, except for part c. When he had skated half way around the circle, he had gone 9.80m. So wouldn't he have gone 19.6m when he skated completely around the circle?

 

[Kurdt]

When he traveled all the way round the circle his displacement would not be 19.6m. Remember displacement is a vector which specifies the position of a particle with reference to an origin or a starting point. If he returns to the starting point then what will the magnitude of the displacement vector be?