Answer to Question #327993 in Mechanics | Relativity for Nzuzi

Question

A hiker travels 4,5 km in a direction 12 degrees south of west and then 7,2 km in a direction 23 degrees west of south.

Determine the hiker’s overall displacement.

Draw each of the hiker’s individual displacement vectors on the same set of Cartesian axes, so that their initial points coincide at

the origin:

:Determine the components of each of these vectors; then use them to find the resultant/overall displacement:

Answer 1

$r_W=4 .5\cos12°+7.2\sin 23°=7.2~km,$

$r_S=4.5\sin12°+7.2\cos23°=7.6~km,$

$r=\sqrt{r_W^2+r_S^2}=10.4~km,$

$\beta=\arctan\frac{r_S}{r_W}=46.5°$ S of W.