Relative Velocity in River Navigation: Solving for Current and Boat Speed

[Jacobpm64]

I'm not sure how to do this problem.. please help..

A river 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 your speed relative to the water?

 

[Päällikkö]

Velocities are vectors.
Draw a diagram and divide the velocities into x and y components.

 

[HallsofIvy]

Almost the same answer: draw a picture showing the vectors: the boat's velocity relative to the shore, the river current's velocity, and the boat's velocity relative to the current. Look at the right triangle you have just drawn and use trigonometry.

 

[Jacobpm64]

I ended up getting
a. 8m/s
b. 10m/s

Is this correct? it looks like a 6,8,10 triangle to me.

 

[Päällikkö]

Yes, they are correct.