Question

A small boat leaves the dock at Camp DuNuthin and heads across the Nessie River at 17 miles per hour, relative to the water, at a bearing of S60° 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 speed of the boat will be 12.18 mph, and the angle of its direction measured from the positive x-axis will be 224.3°

What we can say about the boat speed?

First, let's define North as the positive y-axis and east as the positive x-axis.

In this coordinate axis, the angle S 60° W is equal to 210°.

Then the velocity of the boat will be:

v = (17mph*cos(210°), 17mph*sin(210°))

Now we also need to add the speed of the river, which is 6mph to the east, then the final velocity of the boat will be:

v = (17mph*cos(210°) + 6mph, 17mph*sin(210°))

v = (-8.72mph, -8.5 mph)

Then the speed of the boat will be:

|v| = √( (-8.72mph)^2 + (-8.5 mph)^2)  =12.18 mph

And the angle, measured from the positive x-axis, will be given by the arctangent of the quotient between the y-component and the x-component:

Atan(-8.5 mph/-8.72mph) = 224.3°

If you want to learn more about velocity, you can read:

https://brainly.com/question/19365526