Answer to Question #231720 in Physics for eshiii

Question

In dense jungles of equatorial Africa, an explorer leaves her hut. She

makes 80 steps southeast, then 40 steps 600 east of north, then 50

steps due north. Assuming all her steps are equal in length. a) Draw a

sketch, roughly to scale, showing the three vectors and their resultant.

b) Save her from becoming miserably lost in the jungle by calculating

her displacement vector using the method of components that will

make her return to her hut.

Answer 1

a)

b)

$$R_x=80\cos{45}+40\cos{45}=120\cos{45}\\R_y=-80\sin{45}+40\sin{45}+50\\=-40\sin{45}+50\\R=\sqrt{(120\cos{45}^2+(-40\sin{45}+50)^2}=23\\ \theta=\arctan{\frac{-40\sin{45}+50}{120\cos{45}}}=14\degree\text{ N of E}$$