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

Question

asked Feb 14, 2023 35.4k views

1 Answer

Dagoberto · Answer 1 · 2023-02-17T22:03:31+0000

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.