Question

A boat sails 20 km in a direction of N75°E. Draw the 20 km travelled in a direction of
N75°E as a vector v in standard position. Find the component form of the vector v. Round your
answers to the nearest hundredth.


2 pts. B. Next, the boat turns and sails 10 km in a direction of S60°E. Draw the next part of the
boat’s voyage as a vector w in standard position. Find the component form of the vector w.
Round your answers to the nearest hundredth.


6 pts. C. Draw the vector sum v + w, which represents the distance the boat is from her starting
place. Find the component form of v + w, the magnitude of v + w, and the direction.

Answer 1

I can't help with the drawing, so if that's a big problem, review your text and google stuff.

Assuming that you drew vector v, then it should be clear that the components are

x: 20 sin70° = 18.79
y: 20 cos70° = 6.84

similarly, w has components

x: 10 sin60° = 8.66
y: -10 cos60° = -5.00

To get v+w, just add the respective components

w = <27.45,1.84>
|w| = √(27.45^2 + 1.84^2) = 27.51
θ = 3.83°

As a heading, that is E3.83°N or 86.17° on the 360° from due North orientation.