Answer to Question #235144 in Mechanics | Relativity for Pain

Question

Solve the problem below. One attachment is acceptable (a picture or a word file or a pdf file). Show your complete solution.

A spelunker is surveying a cave. She follows a passage 180 m straight west then 210 m in a direction 45 east of south, and then 280 m at 30 east of north. After a fourth unmeasured displacement, she found herself back where she started. Determine the magnitude and the direction of the fourth displacement.

a. Horizontal component of the fourth displacement. 

b. Vertical component of the fourth displacement.

c. Magnitude of the fourth displacement.

d, Direction of the fourth displacement.

Answer 1

1)

$CO_x=CB_x+AB_x-OA=CB\sin 30°+AB\cos 45°-OA=108.5~m,$

2)

$CO_y=CB_y-AB_y=CB\cos30°-AB\sin45°=94~m,$

3)

$CO=\sqrt{CO_x^2+CO_y^2}=143.6~m,$

4)

$\theta=\arctan \frac{CO_y}{CO_x}=40.9°$ south of west.