[Coda]

Originally Posted by Potironette

Although, I'm confused about the t variable. Since it's how long the system has been accelerating in total, what is how long it takes for the platform to hit the ball :o?

Sorry, I was ambiguous -- there's two different things called "system" in discussion here: the system of moving objects, and the system of equations describing them.

In each equation, t is how long the object has been in motion.

Solving the equations together as a system means that you're looking for the value of t that makes the two equations coincide. To be rigorous you should use a subscripted variable like t_1 like I had mentioned to represent that you're looking for a specific time. (By convention, t_0 would be the time at which you start watching, and for these simple exercises you choose your timeline so that t_0 = 0 to make the math easier.)

Similarly, I was using v for velocity, and rigorously speaking I should have been using v_0 because that represents the INITIAL velocity of the ball, because the velocity changes over time. But in practice you don't have to be that rigorous in your notation as long as everyone involved understands what you're talking about -- but this time, that wasn't true, so I needed to be clearer.