Question

A person walks in the following pattern: 3.1 km north, then 2.4 km west, and finally 5.2 km south. a) Sketch the vector diagram that represents this motion. b) How far and in what direction would a bird fly in a straight line from the same starting point to the same final point?

Answer 1

Answer:

$d = 3.19 km$

direction is given as

$\theta = 41.2 degree$ South of West

Explanation:

Part b)

displacement is given as

$d_1 = 3.1 \hat j$

$d_2 = 2.4 \hat i$

$d_3 = 5.2(-\hat j)$

now we will have

$d = d_1 + d_2 + d_3$

$d = 2.4 \hat i + (3.1 - 5.2)\hat j$

$d = 2.4 \hat i - 2.1 \hat j$

total displacement is given as

$d = \sqrt{2.4^2 + 2.1^2}$

$d = 3.19 km$

direction is given as

$tan\theta = \frac{-2.1}{2.4}$

$\theta = 41.2 degree$ South of West