Question

The Gulf Stream off the east coast of the United States can flow at a rapid 3.9 m/s to the north. A ship in this current has a cruising speed of 11 m/s . The captain would like to reach land at a point due west from the current position.

Answer 1

Answer:

72.54 degree west of south

Explanation:

flow = 3.9 m/s north

speed = 11 m/s

to find out

point due west from the current position

solution

we know here water is flowing north and ship must go south at an equal rate so that the velocities cancel and the ship just goes west

so it become like triangle with 3.3 point down and the hypotenuse is 11

so by triangle

hypotenuse ×cos(angle) = adjacent side

11 ×cos(angle) = 3.3

cos(angle) = 0.3

angle = 72.54 degree west of south

Answer 2

Answer:

$angle = 69.23$ degrees west of south

Explanation:

The ship should go to the south at an equal rate as the water flows north so the velocities balance and the ship just move west.

As far as the water is concerned, the ship goes 3.9 m / s to the south, but much remains to the west. To find out that the triangle is drawing. 3.9 m/s point down side  and the hypotenuse is 11cos(angle) = \frac{adjacent}{hypotaneous}.

$angle = cos^{-1}(\frac{adjacent}{hypotaneous})$

$angle = cos^{-1}(\frac{3.9}{11})$

$angle = 69.23$ degrees west of south