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

`d = 3.19 km`

direction is given as

`\theta = 41.2 degree` South of West

Step-by-step 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 = √(2.4^2 + 2.1^2)`

`d = 3.19 km`

direction is given as

`tan\theta = (-2.1)/(2.4)`

`\theta = 41.2 degree` South of West