displacement and distance

Question

1. A student starts at the origin and ends up at a position 500 m north of the origin. She knows she walked 250 m straight west, but then she was blindfolded and led to the final position. Assume she walked a straight path for the hidden leg of the trip. What is the displacement vector of her movement?

Answer 1

A picture of this scenario might look like this:

You are trying to find the length (magnitude) of "d" and the angle θ (direction) of "d".

Using the Pythagorean Theorem, d = √250² + 500² = 559.017 m

Using trig, tan(θ) = 500/250 so θ = tan^-1(500/250) = 63.435° This direction, from a navigation perspective is typically given as so many degrees off of the North (or South) direction. So it could be given as 26.565° East of North which is noted as N26.565°E

You should round as appropriate.