Question

A hiker travels 12 km in a direction of 50 degrees west of north. What are the north and west components of this displacement?The options for West are, 4.4, 17.1, 9.2, 34

Answer 1

Given:

A hiker travels 12 km in a direction of 50 degrees west of north.

To find:

The north and west components of displacement.

Step-by-step 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:

`N=OPcos\theta=12\text{ km}* cos50\degree=7.71\text{ km}`

The west component of displacement is given as:

`W=OPsin\theta=12\text{ km}* sin50\degree=9.19\text{ km}\approx9.2\text{ km}`

Final answer:

The north component of displacement is 7.71 km and the west component of displacement is 9.2 km.