Vectors
posted by Tarkan .
a river is 2 km wide and flows at 4km/h. a motorboat has a speed of 10 km/h in still water and heads out from one bank. a marina is directly across the river, on the opposite bank. if the motorboat heads directly toward the marina, how far downstream from the marina will be on the other bank?

You don't really even need vectors for this. It takes 2/10 hours to cross the river. In that time, the boat drifts downstream 2/10*4 = 4/5 km.
Now, if you want to find the heading needed to get straight across the river, then you need some vectors.