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Old Aug 27th 2008, 09:08 PM   #1
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Question Relative velocity

Water in a river flows at constant speed U parallel to the banks which are a distance b apart. A boat which travels at speed V is to cross the river, from one bank to a point directly opposite on the other. In what direction should it head and what will be the crossing time?

This topic was covered in about 20 mins in class and I am unsure and confused about the whole deal. Any help will be greatly appreciated!
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Old Aug 29th 2008, 06:58 AM   #2
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Originally Posted by Tulip007 View Post
Water in a river flows at constant speed U parallel to the banks which are a distance b apart. A boat which travels at speed V is to cross the river, from one bank to a point directly opposite on the other. In what direction should it head and what will be the crossing time?

This topic was covered in about 20 mins in class and I am unsure and confused about the whole deal. Any help will be greatly appreciated!
Draw a diagram!!

You want the vector sum of the water velocity and boat velocity to be a right-triangle ..... The hypotenuse is length V and one side is length U.

The angle the boat needs to head at is $\displaystyle \theta$ measured from the river bank in an upstream direction such that $\displaystyle \cos \theta = \frac{U}{V}$.

The speed of the boat is the length of the other side of the right-triangle: $\displaystyle \sqrt{V^2 - U^2}$.

Therefore Time $\displaystyle = \frac{b}{\sqrt{V^2 - U^2}}$.
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