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Deceleration's 100 math problems thread!; Absolute torture...
Topic Started: Aug 4 2011, 04:22 AM (5,622 Views)
Brayzure
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The Analytic Commander

You know, I was sitting here, BOUNCING in my chair, waiting for you to reply. How often do you post questions?
 
Deceleration
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Coreling Conquerer

Whenever I think of one, or I find one in a test of math book that I feel like stealing, with some modifications.
 
Camo5
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Resident BorgCube
I pondered over the problem, and if it hadn't been at a right angle, it would not have been possible to solve. I only would have had 1 side or 2 angles
 
Brayzure
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The Analytic Commander

Yes, it would have been impossible. I used the Law of Sines when I had 3 angles and 1 side (I only needed 2 angles really).
 
Deceleration
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Coreling Conquerer

Ahh, Question 10!

An unusual Gamma-Ray Burst (GRB) kills every living thing onboard the freighter P.T.C. Strainer and wipes out the data banks of the ship's navigational AI. To determine the freighter's position, the AI decides to find its bearing from the galaxy's core. The Galactic Core is 10 degrees to the right of the direction in which the freighter is traveling. A few hours later, the freighter has traveled 20 light-years, and the Galactic Core is now 10.5 degrees to the right. How close will the freighter get to the Galactic Core, assuming it maintains a straight path?
 
Brayzure
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The Analytic Commander

The closest the Strainer will get to the galactic core is 72.526 light years. I can give the distance from the core at each point the data was logged if you want. The very first log (Time of Death) it was 417.658 light years away. The second log, after a few hours had passed, the Strainer was then 397.977 light years away.

EDIT: I would like to know how exactly the freighter was traveling at a super-luminous velocity and the AI could still get accurate measurements?
Edited by Brayzure, Sep 30 2011, 09:01 AM.
 
Deceleration
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Coreling Conquerer

I was a bit off, but whatever. I'll still say you got it right. For the next two, one will be easy, and one harder. And the ship is a special ship, leave it at that.

Also, I think I misnumbered the questions, please ignore that.

Question 11

If the Earth is exactly 92,818,600 miles away from the sun, and its orbit is perfectly circular, how fast does the Earth move in miles per hour? In relation to the sun, of course.

Question 12

An artillery gun on the deck of a battleship 15 meters above sea level fires a test shot at 2000 m/s at an angle of 30 degrees, how far out will the shot land? Include the curvature of the Earth in your calculations, please.
 
Brayzure
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The Analytic Commander

Question 11: The answer is 33,287.47 mph.
Question 12: For the life of me, I cannot find an equation to model the trajectory of the artillery shell!

EDIT: I have the distance, but it does not include the curvature of the Earth. 181.536 km.
Edited by Brayzure, Oct 2 2011, 11:28 AM.
 
Deceleration
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Coreling Conquerer

For question 11 I got something else. Did you forget that 92,818,600 miles is the radius of the Earth's orbit?

As for Question 12, calculate the vertical and horizontal velocities and trajectories separately. And the Earth curves down 4.9 meters every 8 kilometers.
 
Brayzure
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The Analytic Commander

Oh dear, it does seem I calculated it to be the diameter. Simple enough fix. 66,574.94 mph.
Next question. The curvature of the Earth would only affect the distance by around half a kilometer, if that. So in that sense, it seems almost trivial. However, I still have no idea how to solve it; I used a formula.
 
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