Question

A wildlife researcher is tracking a flock of geese. The geese fly 4.5km due west, then turn toward the north by 50? and fly another 4.0km . How far west are they of their initial position? What is the magnitude of their displacement?

Answer 1

The geese fly west 4.5 km, then northwest a further 4 km.

First step is to draw a large, clear diagram.

We can use Pythagoras to calculate the distance west in the second piece. Call the east-west and north-south sides of the triangle x (they are the same), and we get 4^2 = x^2 + x^2 = 2x^2.

2x^2 = 16

x^2 = 16/2

x =2.828 km.

That means the geese are 5+ 2.828 = 7.828 km west of their original position.

We will need to use the sine rule and the cosine rule to find the magnitude of their displacement from the origin:

a^2 = b^2 + c^2 -2bc cos A

Where a is the displacement, b is 4.5 km, c is 2.828 km and angle A is 140 degrees.

a^2 = 4.5^2 + 2.828^2 - 2*4.5*2.828cos 140=47.74 km

a=6.90 km