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

see attached figure,

A girl walks from origin as shown in figure. firstly, she walks 4km towards west.so, OA = 4km

in vector form,

$\vec{OA}=-4\hat{i}$

then, she walks in a direction 30° east of north. so, AB = 3km

in vector form,

$\vec{AB}=3sin30^{\circ}\hat{i}+3cos30^{\circ}\hat{j}$

$\vec{AB}=1.5\hat{i}+1.5\sqrt{3}\hat{j}$

now, displacement, $\vec{OB}=\vec{OA}+\vec{AB}$

= $-4\hat{i}+1.5\hat{i}+1.5\sqrt{3}\hat{j}$

= $-2.5\hat{i}+1.5\sqrt{3}\hat{j}$

magnitude of displacement= 3.6km