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.

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