A woman walks 213 m in the direction 55.9°east of north, then 340 m directly east

directly-east

#1

A woman walks 213 m in the direction 55.9°east of north, then 340 m directly east. Find the difference between the distance the woman walks and the magnitude of her displacement. (Answer in m.) The correct answer is: 23.0 m

Answer:

Let there be two vectors A(which is the first movement) and B(which is the second movement)

Let us take the Cartesian coordinate system with x-axis as i and y axis as j.
And,
|A|=213
|B|=340

The total distance walked is the sum of the two magnitudes
D=213+340= 553m

To find the displacement, we have to find the coordinates of the final position of the woman.

which is,
S= 213 {sin(55.9degrees) i + cos(55.9degrees) j} + 340 i

Finding the magnitude of the displacement vector S = 119.41 j + 516.36 i
|S|=529.98~530

So, difference between distance and displacement magnitude is =D-S=553-530=23 m