Question

The Gulf Stream off the east coast of the United States can flow at a rapid 3.8 m/s to the north. A ship in this current has a cruising speed of 8.0 m/s . The captain would like to reach land at a point due west from the current position.

At this heading, what is the ship's speed with respect to land?

Answer 1

61.6° west of South

Step-by-step explanation:

The ship goes to the south at an equal rate just like water flows to the north. Thus, the velocities would balance making the ship move towards the west.

Since we're dealing with water, the ship goes 3.8 m / s to the South, but a lot still remains to the west. Finding this would require us drawing a triangle. 3.8 m/s point down side and the hypotenuse is 8

cos(θ) = [adjacent/hypotenuse]

Cos θ = 3.8/8

Cos θ = 0.475

θ = cos^-1 (0.475)

θ = 61.6°

Therefore the angle is 61.6° west of South.