Find boat's true speed and heading?

Question

A small boat leaves the dock at Camp DuNuthin and heads across the Nessie River at 18 miles per hour, relative to the water, at a bearing of S61° W . The river is flowing due east at 6 miles per hour. What is the boat's true speed and heading? Round the speed to the nearest mile per hour and express the heading as as a bearing with the angle rounded to the nearest tenth of a degree.

Answer 1

The combination of the true speed and heading is the net velocity, which is the vector sum of the boat's velocity and the velocity of the water. Using an angle of zero for due north, the boat's velocity (relative to the water) is 18mph at an angle of 241 degrees. The water velocity is 6mph at an angle of 90 degrees.

To find the vector sum:

First find the x and y components of each vector. ( x and y can be defined any way you like--a convenient option would be +x = east, and +y = north.)

Add the x and y components, and then find the angle, which is the tangent of x/y.

Draw a Picture to visualize and to see the approximate solution.