Geometric Vectors

[Macleef]

1. The problem statement, all variables and given/known data

A river is 2 km wide and flows at 6 km/h. A motor boat that has a speed of
20 km/h in still water heads out from one bank perpendicular to the current.
A marina lies directly across the river on the opposite bank. Use Geometric
Vectors to solve this problem.

a. How far downstream from the marina will the boat reach the other bank? (Answer: 0.6 km)
b. How long will it take? (Answer: 6 min)


2. Relevant equations

The sine and cosine laws.


3. The attempt at a solution

Here's what I've done so far, I drew the diagram to the problem. I'm not sure if it's correct or not:

http://i30.tinypic.com/t5q87r.png

And now, I don't know what to do to answer the questions.

[pooface]

I dont think the diagram is correct. The boat at 20km/h sets out horizontally (perpendicular to the current BUT since the current is pushing it down, the boat gets displaced diagonally. The boat will still reach the other side, but not in a straight line therefore missing the marina. That is why the first question asks how far DOWNSTREAM from the marina does the boat reach the other bank.