a boat travels at a constant speed of 20 knots due east. The current flows from a bearing of S68°E at speed of 5 knots, headwind is blowing toward the west at speed 6 knots. Where will you end up?

Answer 1

I can't tell you where you end up because that depends on how long you travel. But I can tell you which direction you will end up going. To do so requires you to add all three vectors together.

First consider right as positive and up as positive. You can add the +20 (which is east) and the -6 (which is west) to get +14 (14 in the easterly direction)

You can break the vector 5 in the S68°E into two vectors, one going east and one going south, using trig ratios. The one going east, as shown, would be 5sin(68°) which is approx 4.64 knots. The one going south would be 5cos(68°) which is approx 1.87 knots.

You can now add 4.64 to the 14 knots to get 18.64 knots (the total in the easterly direction) and you still have 1,87 in the southerly direction.

You can combine these together using the Pythagorean Theorem to get a total.

Total speed = √[(18.64)² + (1.87)²] = √350.806 = 18.73 knots.

To find the direction, use tan^-1(1.87/18.64) = 5.74° south of east. Since 90° - 5.74° = 84.26° then it can be written as S84.26°E