# Math Help - Geometric Vectors

1. ## Geometric Vectors

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?
b. How long will it take?

Im realy not sure about how to do this...

2. Originally Posted by a.a
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?
b. How long will it take?

Im realy not sure about how to do this...
I've attached a sketch of the situation.

The boat needs $t=\frac{2\ km}{20\ \frac{km}{h}}=\frac1{10}\ h = 6\ min$ to cross the river.

During these 6 minutes the boat floats $d=\frac1{10} \ h \cdot 6\ \frac{km}{h} = 0.6\ km = 600\ m$

Actually the boat is moving perpendicularly to the current through the water. But a spectator ashore will observe a course according to the red line (cog).