Answer to Question #232786 in Physics for Eshiii

Question

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

makes 80 steps southeast, then 40 steps 60

Answer 1

An explorer in the dense jungles of equatorial Africa leaves his hut. She makes 80 steps southeast,  then 40 steps 60° 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.

Solution

a) The sketch is below:

b) Find the corresponding components:

$$A_x=80\cos45°=56.6,\\ A_y=-80\sin45°=-56.6.\\ B_x=40\sin60°=34.6,\\ B_y=40\cos60°=20.\\ C_x=0,\\ C_y=50.\\ R=\sqrt{(A_x+B_x+C_x)^2+(A_y+B_y+C_y)^2}=\\=92.2,\\\space\\ \theta=\arctan\frac{A_y+B_y+C_y}{A_x+B_x+C_x}=8.4°\text{N of E}.$$

To return home, she must make 92 steps at 8.4° S of W.