Question

Strangely, your campsite has an xy coordinate system scratched out in the surrounding ground. A fellow camper is to walk away from you (at the origin) in a straight line for 22.0 m at an angle of −47.0°. (The negative sign means that the angle is measured clockwise from the positive direction of the x axis.) Let A→ represent that walk. The camper then turns by angle ϕ in the counterclockwise direction and walks 17.0 m in a straight line. Let B→ represent that walk. The camper ends up on the x axis as shown in the figure below

Fellow camper Example 3.2.4 Figure 1

Let C→ represent your walk to meet up with the camper. The direction of C→ is obviously along the x axis, but what is its magnitude?

Answer 1

In x direction, we have

C*cos 0 = 22 * cos (-47) + 17 cos $\phi$

In y direction, we have

C* sin 0 = 22 * sin (-47) + 17 sin $\phi$

as sin 0 = 0 , we get

-16.089 + 17 sin $\phi$

$\phi$ = arcsin (0.94645)

$\phi$ = 71.1646 degree

or

$\phi$ 71.17 degree