In going from one city to another, a car travels 120 miles west, 50 miles north, and 40 miles southeast. How far apart are the two cities? (displacement)

Question

In going from one city to another, a car travels 120 miles west, 50 miles north, and 40 miles southeast. How far apart are the two cities? (displacement)

Answer 1

This is a start.

 

120 west = <-120, 0>

50 miles north = <0, 50>

 

This puts the car at <-120, 50>

 

Southeast is at 45°. With 40 miles the vector is <20√2, -20√2>

 

The car is now at <-120 + 20√2, 50 - 20√2>.

 

The decision is now whether to use Pythagoras with the radical or the decimal value.