Given:
A hiker travels 12 km in a direction of 50 degrees west of north.
To find:
The north and west components of displacement.
Explanation:
From the diagram,
The distance traveled by the hiker in a direction of 50 degrees west of north is:
OP = 12 km
The north component of displacement is given as:
[tex]N=OPcos\theta=12\text{ km}\times cos50\degree=7.71\text{ km}[/tex]The west component of displacement is given as:
[tex]W=OPsin\theta=12\text{ km}\times sin50\degree=9.19\text{ km}\approx9.2\text{ km}[/tex]Final answer:
The north component of displacement is 7.71 km and the west component of displacement is 9.2 km.
