Answer to Question #141696 in Physics for Dahyuun

Question

A gardener is shifting the scissor to cut a tree. His first displacement is 1.0m, East. Next is 2.0m 45 degrees Southeast, and the third is an unknown. His resultant displacement is 6.0m directly East. Determine the magnitude and direction of his third cutting.

Answer 1

$$\bold{s_1+s_2+s_3=s}\\(6,0)=(1,0)+(2\sin{45},-2\cos{45})+(s_{3x},s_{3y})\\(s_{3x},s_{3y})=(3.49,1.41)\ m$$

$$s_3=\sqrt{1.41^2+3.49^2}=3.76\ m$$

$$\theta=\arctan{\frac{1.41}{3.49}}=22\degree \text{ N of E}$$