A woman walks 250 m in the direction 48° east of north, then 165 m directly east. Find (a) the magnitude and (b) the angle (from due east) of her final displacement from the starting point. (c) Find the distance she walks.

(a)  

(b)

(c)

Explanation:

Given data

The Woman walks 250m in 48° east of north

Then 165m due to east

Let east be the +x axis and the north is +y direction

So the two displacements is written in polar form as:

d₁=250∠(90°-48°)=250∠42°

d₂=165∠0°  

All angles are measured in counterclockwise from +x direction

So the total displacement is given dot product as:

Part (a)

The magnitude of women total displacement

Part (b)

The angle of woman displacement from her starting point is

Part (c)  

The Total distance that the women walks is given as:

double the distance = divide strength by 4