What is the Velocity of the River's Current?

[future_vet]

Homework Statement

A boat whose speed in still water is 1.70m/s must cross a 260 meter wide river and arrive at a point 110 metres upstream from where it starts. To do so, the pilot must head the boat at a 45 degrees upstream angle. What is the speed of the river's current.

Homework Equations

According to my lecture, I believe the equation should be sin Theta = Vws/Vbs
Vws being the water's current, and Vbs the boat's speed. However, I don't know where the river's width comes in.

The Attempt at a Solution

Sin 45 = Vws/1.70 m/s
Vws = Sin 45 x 1.70
Vws = 1.20 m/s.

Would this be correct?

THANKS!

 

[future_vet]

No ideas?...

 

[hage567]

I don't believe you are correct. You are not taking into account that you want to land 110 m upstream. Draw a picture. You'll see that at the angle of 45 degrees, the distance traveled along the river bank (in direction of current) is more than 110 m. This is necessary because the river will push the boat downstream. What you have calculated is the upstream component of the boat's velocity, not the velocity of the river current.