danago

Gold Member

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**1. Homework Statement**

A Family has a boat which can travel at 12 m/s in still water. They are using it to reach a point 500m downstream on the other side of a river 300m wide, and flowing at 4 m/s. What heading must they take, relative to their starting point, in order to reach their destination?

**3. The Attempt at a Solution**

I first drew a triangle, with the side parallel to the river banks 500m, and the side perperndicular 300m. From there, i found that to end up 500m downstream, the resultant direction of travel should be ~59 degrees from the perpendicular (or 31 degrees from the bank).

The rivers current plus the boats motion should result in a velocity in the direction of 59 degrees. So:

[tex]

\left( {\begin{array}{*{20}c}

4 \\

0 \\

\end{array}} \right) + \left( {\begin{array}{*{20}c}

{12\sin \theta } \\

{12\cos \theta } \\

\end{array}} \right) = \lambda \left( {\begin{array}{*{20}c}

{100\sqrt {34} \sin 59} \\

{100\sqrt {34} \cos 59} \\

\end{array}} \right)

[/tex]

I solved for theta, and found that it equals 49 degrees. So i concluded that to end up 500m downstream, the boat should set off at 49 degrees to the perpendicular of the banks.

Im unsure if that is correct. Also, is there a better way i should have gone about it?

Thanks,

Dan.