Question

A public transportation department measures the distance from a location using displacement vectors. To ride the bus to work for a discounted amount, you have to travel further than 1.5 mi. (7,920 ft.) from your home. Your cell phone calculates that when you walk to work, you go 1,600 ft. south and 6,300 ft. west. What is the magnitude of the displacement vector from your home to work, and will you be able to ride the bus for the discounted rate?

Answer 1

6,500 ft., no discount

Answer 2

Using Pythagoras theorem,

Altitude^2 +  Base^2  = Hypotenuse^2

Altitude = Distance Traveled South

Base = Distance traveled west

Hypotenuse = Displacement vector

Putting the values,

1600^2 + 6300^2 = 42250000

Displacement vector = (422550000)^1/2 = 6500

So, no discount.