A hiker walks 50 miles 55 degrees south of west. How far did she walk west?

Select one:

a. 28.7 miles

b. 40.9 miles

c. 35.4 miles

d. none of the above

She walked 28.7 miles west ⇒ answer a

Explanation:

A hiker walks 50 miles 55 degrees south of west

That means the magnitude of her displacement is 50 miles

55 degree south of west means the angle between her displacement

direction and the west is 55°

We need to find how far she walk west

Her walk to west is the horizontal component of her displacement

West is adjacent to the angle of direction

If the magnitude of her displacement is R and its direction is Ф, then

→ The horizontal component = R cos Ф

→ R = 50 miles, Ф = 55°

→ The horizontal component = 50 cos (55) = 28.7 miles

The horizontal component represents her walk to the west

She walked 28.7 miles west