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Find the Velocity - a Vector Problem

```Date: 09/25/2002 at 20:40:54
From: Danbi
Subject: Physics

A river flows westward at 8 m/s. A person wants to go directly across
the river so that the resultant velocity is 12 m/s northward.  Find
the velocity of the motorboat that would be required to achieve this
resultant velocity.

This is a question my Physics teacher posed to the class for our
homework assignment. I'm not sure on how to go about solving it. Any
help would be much appreciated.
```

```
Date: 09/26/2002 at 16:52:21
From: Doctor Jeremiah
Subject: Re: Physics

Hi Danbi,

Its a vector problem.

You can't go straight north in a boat with a current pushing you west.
You must go northeast. The east component of the velocity must be the
same as the current's velocity in order to cancel it out and end up
with a straight north direction.

The velocity of the boat would look like this:

^
|
|
|
|
|
12
|
|
|
|
|
+----8---->

So combine these velocities into a single vector and find its
magnitude. The magnitude of the combined vector is the speed that the
boat must make in the northeast direction.

Let me know if you have more questions.

- Doctor Jeremiah, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Linear Algebra

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