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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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