Vector Application Problem

Question

My kittens, Annie and Josie, are pushing a ball, Annie with a force magnitude of 80 N in a direction of 133°, and Josie with a magnitude of 95 N in a direction of 290°. If a third cat wants to prevent the ball from moving, with what magnitude and direction of force must she push?

Answer 1

Changing to vectors

v1 = 80cos(133)i+80sin(133)j

v2 = 95cos(290)i+95sin(290)j

v1+v2 = -22.06i -30.763j

The third cat will need to push in the opposite direction

v3 = 22.06i +30.763j

|v3| = 37.855 θ = 54.36°