Answer
6.6 km
The description of the problem is shown in the attached figure, where the line "d" represents the final displacement vector.
First, the trekker walked 3.3km in a 40 ° direction, as shown in the figure. We can write this vector in its Cartesian coordinates:
[tex]-3.3sin (40)x + 3.3cos (40)y[/tex]
Then the hiker walked 3.4 km in a 60 degree northwest direction.
We can write this as a vector in its Cartesian coordinates:
[tex]-3.4sin (60)x + 3.4cos (60)y[/tex].
When adding this two vectors we will obtain the final displacement "d"
[tex]d = [- 3.3sin(40) -3.4sin (60)]x + [3.3cos(40) + 3.3cos (60)]y\\[/tex]
[tex]d = -5.07x +4.23y\\[/tex]
To obtain the magnitude of this vector we calculate its module:
[tex]\sqrt{5.07 ^2 +4.23 ^ 2}[/tex]
Then the magnitude of the final displacement was:
6.6 km
