Question

1.) A jogger runs directly east for 4 km, then turns and goes northwest for 9 km. He then travels directly south for 3 km. How far is he from the starting point? (km)

2.) In what direction is he from the starting point(measured as an angle counterwise from the east axis, units are deg)? (Northwest is the direction lying exactly half way between north and west.)

Answer 1

Part 1) - Solution

The magnitude of the final vector position of the jogger will tell us how far is he from the starting point. The final vector position can be expressed as,

In the following figure, we show the vectors , , and

The next step is represent all vectors in an analytical way,

inserting all data into eq. (1), we have

The magnitude is

or

The jogger is 4.11 km from the starting point.

Part 2) - Solution

Let be the angle requested, then

We can use geometry to find the angle ,

thus,

or

The jogger is in a direction 125° from the starting point measured counterwise from the east axis.