Question

A person walks in the following pattern: 3.0 km north, then 2.1 km west, and finally 4.2 km south. (a) How far and (b) at what angle (measured counterclockwise from east) would a bird fly in a straight line from the same starting point to the same final point?

Answer 1

Answer:

(a) 2.42 km

(b) 119.74°

Explanation:

(a)

The shortest distance from starting to end point is the hypotenuse

$C=\sqrt{a^{2}+b^{2}}$

Where a is is base and b is height. Substituting 1.2 km for a and 2.1km for b then

$C=\sqrt{1.2^{2}+2.1^{2}}=2.41867732448956 km\approx 2.42 km$

(b)

The angle is given by the $\theta$ as indicated in the sketch

$\theta=\frac {2.1}{1.2}=60.2551187030578\approx 60.26^{\circ}$

Towards East it will be 180-60.26=119.74°