Question

A wildlife researcher is tracking a flock of geese. The geese fly 4.0 km due west, then turn toward the north by 40° and fly another 4.0 km. How far west are they of their initial position? What is the magnitude of their displacement? Knight, Randall D., (Professor Emeritus). College Physics (p. 100). Pearson Education. Kindle Edition.

Answer 1

Answer:

(a). The distance is 7.06 km due to west.

(b). The magnitude of their displacement is 7.51 km.

Explanation:

Given that,

The geese fly 4.0 km due west, then turn toward the north by 40° and fly another 4.0 km.

According to figure,

(a). We need to calculate the distance

Using formula of distance

$AD=AB+BD$

Put the value into the formula

$D= 4+4.0\cos40^{\circ}$

$D=7.06\ km$

The distance is 7.06 km due to west.

(b). We need to calculate the magnitude of their displacement

Using formula of displacement

$AC=\sqrt{(CD)^2+(AD)^2}$

Put the value into the formula

$AC=\sqrt{(4.0\sin40)^2+(7.06)^2}$

$AC=7.51$

The magnitude of their displacement is 7.51 km.

Hence, (a). The distance is 7.06 km due to west.

(b). The magnitude of their displacement is 7.51 km.