Question

You fly 32.0 km in a straight line in still air in the direction 35.0º south of west.

(a) Find the distances you would have to fly straight south and then straight west to arrive at the same point. (This determination is equivalent to finding the components of the displacement along the south and west directions.)

MCQ Options:
What is the component of the displacement along the south direction?
a) 32.0 {km} ⋅ cos(35.0^∘)
b) 32.0 {km} ⋅ sin(35.0^∘)
c) 32.0 {km} ⋅ tan(35.0^∘)
d) 32.0 {km} ⋅ cot(35.0^∘)

Answer 1

To find the distances you would have to fly straight south and then straight west, you multiply the total distance (32.0 km) by the cosine and sine of the angle south of west, respectively.

Step-by-step explanation:

To find the distances you would have to fly straight south and then straight west, you need to find the components of the displacement along the south and west directions.

To find the south component, you multiply the total distance (32.0 km) by the cosine of the angle south of west. So the component of the displacement along the south direction is 32.0 km * cos(35.0°).

To find the west component, you multiply the total distance (32.0 km) by the sine of the angle south of west. So the component of the displacement along the west direction is 32.0 km * sin(35.0°).