A wildlife researcher is tracking a flock of geese. The geese fly 5.0

Question

A wildlife researcher is tracking a flock of geese. The geese fly 5.0 km due west, then turn toward the north by 45 ∘ and fly another 3.5 km .

How far west are they of their initial position?

What is the magnitude of their displacement?

Answer 1

Start with a simple sketch. a) The displacement in x is -5 - 3.5 cos 45° = 7.5 m West.

b) The total x component is again (-) 7.4₇ m and the displacement in y is 3.5 sin 45° = (+) 2.4₇ m. The square root of x² + y² is 7.9 m. [The same result is obtained with the law of cosines]