Question

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

Answer 1

Let the headings O and B be the girl's initial and final positions. Then, the position of the girl can be shown.

now we have:

`vec(OA) = -4hati`

`vec(AB) = hati |vec(AB)| cos60° + hatj |vec(AB)|sin60°`

= `hati xx 3 xx (1/2) + hatj xx 3 xx (sqrt3/2)`

= `(3/2)hati + ((3sqrt3)/2)hatj`

By the triangle rule of vector addition, we have:

`vec(OB) = vec(OA) + vec(AB)`

= `(-4hati) + (3/2hati + (3sqrt3)/2hatj)`

= `(-4 + 3/2)hati + (3sqrt3)/2hatj`

= `((-8 + 3)/2)hati +(3sqrt3)/2hatj`

= `(-5)/2hati + (3sqrt3)/2hatj`

Therefore, the girl's displacement from her initial point of departure is `(-5)/2hati + (3sqrt3)/2hatj`.