Question

A jogger runs 5.0 km on a straight trail at an angle of 60° south of west. What is the southern component of the run rounded to the nearest tenth of a kilometer?

Answer 1

The southern component of the jogger's path is given by:

`S_y = S \sin \theta`

where

`S=5.0 km` is the total distance of the jogger's run

`\theta=60^(\circ)` is the angle with respect to the horizontal direction

Substituting numbers into the equation, we find

`S_y=(5.0 km)\sin (60^(\circ))=4.33 km`

and the direction is south.

Answer 2

Without rounding off, the answer is -4.33. Since, the southern component of the run of the jogger should be rounded to the nearest tenth of a kilometer, then the answer is -4.3. The answer is negative because it is going south.