Magnitude and Displacement

Question

1. A football player runs 12m North and 4m East

a) what is the overall magnitude of the displacement of the football player?

b) what is the direction of the overall displacement of the football player? Be as specific as possible

Answer 1

This question relies on two things, one of them less obvious than the other.

The less obvious bit is that we're asking about DISPLACEMENT not DISTANCE. If you run 12m north then 4m east, you've traveled 16m in total. That's the distance, and it depends on your path. The displacement, meanwhile, is the shortest path from start to finish (as the crow flies).

You could travel the 12m north, then 30m west, then 34m east and you would still have the same displacement as the original problem, since your starting and ending points haven't changed, even if your new path covered more ground.

So we know we need to find the path as the crow flies (a straight line) from start to finish. Luckily for us, north and east are at a 90 degree angle, so we can draw this problem as a right triangle with legs that are 12m and 4m long respectively.

4m

____

| /

12m | / d=?

| /

|/

At this point, all that's left is to apply the Pythagorean theorem to get our unknown:

a² + b² = c²

(4)² + (12)² = d²

d = sqrt( 16 + 144 ) = 4*sqrt(10) = About 12.6 meters