Application of Vectors

Question

A sailboat captain has set her course due west at a speed of 6 meters per second. The wind is blowing due north at a rate of 2 meters per second.

1. The direction of the sailboat's travel, considering the wind factor, will be
2. The actual speed of the sailboat in the direction of travel is 

Answer 1

Sketch two vectors (direction as given in the problem, and length representing the magnitude - the speed/rate in this case).

If you use these two vectors to create a parallelogram (a rectangle in this case), the diagonal of the parallelogram will be the resultant vector (i.e. the actual speed and direction of the sailboat).

Can you see that you can now use trigonometry to calculate the angle, x, and Pythagoras' Theorem to calculate the length (magnitude) of the resultant vector?

tan(x) = ²/₆

x = tan^-1(²/₆) = 18.4°

Remember to add 270° (the clockwise angle from due North to due West) to give this angle as a bearing: 288.4°

Use Pythagoras' Theorem to calculate the actual speed of the sailboat: Speed = √(6² + 2²) = 6.32 meters per second