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Originally Posted by Potironette
Ohh, so it can happen because if y = 10, then
0 = -v*t - (1/2)g*t^2
v*t = - (1/2)g*t^2
v = - (1/2)gt
-v = (1/2)gt
and the velocity will be a number so time can pass! And the negative is probably because gravity and the velocity upward are not going in the same direction?
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Um... actually the negative is because I wasn't paying attention to the signs I was using in other places, and it should have been a +. But you derived the correct conclusion from it anyway!
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So if y = d
Ball: 0 = -v*t - (1/2)g*t^2
Platform: d = d' + (1/2)a*t^2
at' = v where t' is how much time the platform has been accelerating in total
And then to plug that into 0 = -v*t - (1/2)g*t^2
at't = - (1/2)gt^2
a = (-(1/2)gt^2)/(t't)
So... given the time the platform has been moving and given the time it took for the ball to hit the platform, it's possible to find an acceleration for which the ball falls lands on the platform where it started? It looks a lot less convenient than I'd imagined in the beginning!
Uh, granted I have no clue if this is messed up or not, or if it's a quadratic equation. It doesn't really look like one, I think.
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t is always how long the system has been accelerating in total. You don't need to define a t'. You might choose to define a t_1 or something that specifies a particular time in the sequence (perhaps you might designate it to be the time when the ball meets the platform) but if you do that you would plug it in as a value for the t variable instead of assigning it to the other side of the equation.
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At this point I think it's starting to go in over my head X'D. I don't really understand how equations relate to each other, or what systems are.
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I don't know how old you are or what class you're taking, so I don't know what your background is or what you've already studied. :P
The short version is that if you have multiple equations, then the only relationship between them is that they all have to stay true all the time, and any variable that appears has to have the same value in all of the equations. (Even if you don't know what that value IS.)
If you can solve any of the equations for one of the variables in it, then you can substitute that solution in place of that variable in any of the other equations. Usually when you're solving a system of equations your goal is to do this iteratively until you produce one that's entirely expressed using a single variable.
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Ohh that's really cool! How much of a stretch would it be to say that in the moment a person is being pushed or pulled, their idea of gravity is changed and so they lose their balance?
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THAT starts getting into terms with a t^3 factor, which is called "jerk" and describes the rate of change of force. Humans are pretty good at dealing with forces that change slowly, and you can keep your balance reasonably well if you're given time to adjust your stance.
But if you're saying the box suddenly starts accelerating, then yeah, the person is PROBABLY going to fall over.
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As for the centrifuge, I sadly haven't learned a thing about rotating systems yet, or calculus '~'.
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I didn't expect you to have, which is why I didn't go into any further detail. :P I mentioned that it COULD be done and left it at that.
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Originally Posted by mdom
Coda, you just became 10000x sexier to me
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Sorry, ladies, I'm married.