Displacement Vector Homework: Magnitude & Direction

[Kitty808]

Homework Statement

A runner jogs around a circular track 160 ft in diameter, what is the magnitude of the displacement vector when the runner has completed 1/4 of a lap? 1/2 a lap? What is the direction of the runner's displacement vector at 1/4 and 1/2 a lap? What is the magnitude of the runners displacement vector when a full lap is completed?

The Attempt at a Solution

Ok, I am pretty much clueless on this, even after spending an hour reading my textbook. (I'm -really- bad at physics). I calculated the circumference of the track to be 502 ft which makes 1/4 of the track 125.5 ft. But the online software said that the magnitude of 1/4 of a lap should be 113 ft. How did they get this number. Also the magnitude of a complete lap is obviously 0 ft, but I'm not sure how to go about solving for the directions either. Any help would be appreciated, like I said, I'm pretty clueless XD.

 

[Doc Al]

Make yourself a diagram. Draw an arrow from where the runner starts to where he finishes. That's his displacement vector. Use a bit of trig/geometry to find its magnitude.

 

[Kitty808]

I tried that and only ended up confusing myself more, I can usually figure out displacement vectors for something that's one direction, then another, but this whole circle thing is throwing me off

 

[Doc Al]

Show the diagram that you drew.

Or tell me the coordinates of the runner's starting point and ending point. (I don't know where he starts or whether he runs clockwise or counterclockwise, so I can only guess.)

For example, let's say the radius of the circle was R (with the center at the origin) and that he starts at point (R, 0) and runs 1/4 lap and ends up at point (0, R). What's the distance between those two points?