83. A sailboat travels south at 12.0 km/h with respect to the water against a current 15.0° south of east at 4.0 km/h.
What is the boat's velocity?

The magnitude of the boat's velocity is 8.21 km/h.

Explanation:

We can find the boat's velocity as follows:

Where:

and are the components of the velocity of the water in the x and y-direction

and are the components of the velocity of the boat in the x and y-direction

Since the angle is 15° we have:

Now, the velocity of the boat is:  

Therefore, the magnitude of the boat's velocity is 8.21 km/h.

I hope it helps you!

the answer is 3.1 his answer is wrong mines is right

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west