You are boating on a river that flows toward the east. Because of your knowledge of physics, you head your...?

Question

You are boating on a river that flows toward the east. Because of your knowledge of physics, you head your boat 53 degrees west of north and have a velocity of 6.0 m/s due north relative to the shore.

a. What is the velocity of the current?

b. What is the speed of your boat relative to the water?

Please help me with this problem.
I'm having trouble understanding it.

I asked this question once before, but the answer I received was not helpful.

Answer 1

First of all you need to understand the question. The information give is not very clear so certain assumings are made.

Based on the information given, I assume that the boat is traveling east. The boat is 53º off course because of the current and because of the speed of the current flow the boat travels in an East ward direction.

It can be helpful to draw out a diagram.
Complete the triangle with the horizontal axis. Now you have 37º with the horizontal axis (east direction) with a vector of 6 units.
90º - 53º = 37º
Opposite side = 6 units.

Now find the lengths of the other two sides.

Cos Θ = Adj../ Hyp.
Adj. = Hyp. Cos Θ
Adj. = (6)Cos 37º
Adj. = (6)(0∙798 635 51)
Adj. = 4∙791 813 06
Adj. ≈ 3∙79 m/s. (Water velocity form North to South).

The Hypotenuse of the triangle will be the speed of the boat relative to the water.
H = √(Adj.² + Opp.²)
H = √(4∙791 813 06 ² + 6²)
H = √58∙961 4724
H = 7∙678 637 405
H ≈ 7∙68 m/s