Question

A boat attempts to sail due east at 15km/h, but is taken off course by a current of 5 km/h flowing in the southwest direction. Find the resultant speed of the boat and the bearing on which it travels.

Answer 1

Resultant speed = 12 km/h.

Bearing is 107.14 degrees.

Explanation:

This can be represented by a triangle of velocities with lengths 15 and 5 with the included angle = 45 degrees.

To find the velocity of the resultant we use cosine rule:

v^2 = 15^2 + 5^2 - 2*5*15cos 45

v^2 = 143.934

v = 12.0 km/h to the nearest tenth.

To find the bearing we use the sine rule to find the angle down from due east>

12 / sin 45 = 5/ sin x

sin x = 5 sin 45 / 12 = 0.2946278

x = 17.14 degrees.

Bearing is therefore 90 + 17.14 = 107.14 degrees.