Answer to Question #267434 in Physics for Lea

Question

A force F~ = Fx ˆı + Fy ˆ acts on a particle that undergoes a displacement of ~s = sx ˆı + sy ˆ where Fx = 3 N, Fy = −1 N, sx = 5 m, and sy = 2 m. Find the angle between F~ and ~s.

Answer 1

The angle is

$\theta=\arccos\frac{F·s}{|F|·|s|}=\\\space\\ =\arccos\frac{3·5+(-1)2}{\sqrt{(3^2+(-1)^2)(5^2+2^2)}}=40.2°.$