Question

Sam runs 3.0 miles East, turns left and runs 3.0 miles North and turns right and runs 2.0 miles East. What is the total distance he runs? What is his net displacement? (magnitude in miles and direction as an angle from East towards North.

Answer 1

I believe total distance is 8.0 miles but I am having problems with the net displacement which includes the magnitude and direction.

Answer 2

\[d = \sqrt{N^2 + E^2} = \sqrt{(3^2) + (3+2)^2}\]

Answer 3

The angle can be found as follows:\[\tan(\theta) = \left ( N \over E \right ) = \left( 3 \over 5 \right)\]