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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,742

HI;

This problem appeared in the Bafflers thread as exercise #2 and has some algebraic solutions.

A ship is sailing on a course from the origin. It follows the path y= 3.14 x. It has a speed of 1 / 3 units per second. A submarine is located at (5,0). The sub knows the ship is oblivious to its existence. The sub would like to torpedo the warship. Torpedoes travel at 1 / 2 units per second and travel in straight lines. The sub commander's hobby is mathematics. He fires and sinks the ship! What is the equation of the torpedoes flight?

One solution is to realize that what is required is triangle with one side being the line y = 3.14 x the base being the x axis from 0 to 5 and some line passing through (5,0) and intersecting y = 3.14 x. See fig 1. With the condition that the red line is 1.5 times longer than the other side of the triangle. Let's use Geogebra to solve the problem.

1)Draw the point (5,0) and call it Sub.

2)Enter in the input bar f(x) = 3.14 x

3)Place a slider on the drawing. Set it at Min=0 and Max = 10 with an increment of .1

It should be called a.

4)Enter (a,3.14*a) and call it Ship. Move the slider and you will see the point is constrained along y = 3.14 x.

5)Make a point at (0,0) and call it Start and hide it.

6)Enter Distance[Ship,Sub]/Distance[Start,Ship]

7) Set in options, rounding = 15 decimals, immediately you will see b = some value. That is the ratio of the torpedoes distance to the ships distance.

8)Move the slider using shift arrows until you get b = 1.497666014479171

9)Right click the top part of the slider to get the properties and set the increment to .01

Make sure you click the top part of the slider to select it after pressing close.

10)Press Shift left arrow until you get b = 1.499835795083569 and a = 1.038

11)Repeat 9 but set the increment to .001

12)Repeat the above loop always getting an answer as close to 1.5 as possible and slightly smaller.

I get b = 1.49999993088931 with an increment of 0.000001, how did you do?

13)Draw a line between Ship and Sub using the line tool and read off the equation of that line. I got

See the second drawing to check your work.

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

Hi bobbym

Just a thought.It is nowhere stated that the direction of the ship is the positive part of the line.There is another solution in the other case, I just haven't calculated it yet.

*Last edited by anonimnystefy (2012-03-06 07:22:13)*

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 86,742

We can continue with the same Geogebra program posted in post #1

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

hi bobbym

thought so,but just wanted to mention that there are 2 solutions.

AND i'm on my desktop,so i can maybe hurry up and type down the generating function in the Bafflers.

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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