00:01
In this problem, it'll be useful to take into account the law of conservation of energy.
00:07
We know that both balls have the same velocity, but we don't know if they are identical, meaning do they have the same mass or not.
00:16
So let's set up an equation to represent the energy of some ball m.
00:22
So we're not talking about either of those masses.
00:24
We're talking about some unknown mass at that point, mass m has some gravitational potential energy.
00:31
So that is the mass times gravity times height.
00:36
And it also has some kinetic energy, which is one half times the mass times the velocity squared.
00:46
Now since the velocity is squared, it doesn't matter if it's positive or negative because it'll be positive either way since it's squared.
00:55
So that is our initial condition.
00:57
Now at the bottom, we no longer have a height.
01:00
Height is zero.
01:02
So either if the ball went straight down or if it went back up and then back down, it'll have some kinetic energy but no potential.
01:13
So at the end we have one half times the mass times the final velocity squared.
01:23
And since there is no air resistance, then we know that no energy has been lost in this process...