A new thread! Makes me wonder if I should change the first post XD. Thanks for helping me with this! School's definitely not asking me to answer these questions, but I get pretty confused when I have questions based on what school is telling me.
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No, solving that last step for t results in t = 0, which means that given the initial conditions you put into the system, they start off in contact with each other.
Which is, in fact, what you did by using d in both of those position equations -- what you're calling d is the initial position of the object, and you've used the same position for both of them. You'll notice in my example that I had the ball starting at 10 and the platform starting at 0.
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So.. something like this can't happen? :
I used " d, " with the comma for the platform, since I was worried I'd forget that I was trying to think about positions.
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Ball: y = d - (1/2)g*t^2
Platform: y = e + (1/2)a*t^2
y = d so the ball ends up where it started
Ball: d = d - g*t^2
0 = -g*t^2
meaning that for the ball to hit the ground where it began, no time has passed, since knowing only the initial and final position, it's that the ball has not moved at all.
But..
Platform:
d = e + r where r is the distance between d and e
d = e + (1/2)a*t^2
e + r = e + (1/2)a*t^2
r = (1/2)a*t^2
In this case the time is not zero because this equation has more information on what the ball is doing?
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Nope, there's not. The only thing that makes motion "vertical" is that it's parallel to the direction of gravity. All you have to do is replace g with the acceleration due to gravity in the direction of motion; for horizontal motion, that means g is 0.
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That means that if somehow, there was an accelerating box on the ground moving all around earth somehow, and there was a person in it, the person would feel that gravity was whatever direction opposite where the person was accelerating in? Would they think the ground was the side of the box accelerating towards them and they'd feel like the box was moving to side pushing them against the side of the box on the ground :o? Actually, this reminds me sort of the NASA centrifuge I keep hearing mentions of in class, though I'm not sure how people feel inside there.