 Okay, so the next lab, you're going to shoot a little ball up in the air and try to determine how fast it was shot. We're going to do it two different ways using two different measurements. And I'm going to show you the physics behind there because that's not the point. The point is really something else. So here's the first case. Here's my little ball launcher and there's my ball and I'm going to shoot it up with some initial velocity in the y direction, v0, in that direction. It's a one-dimensional problem so I'm not going to use vectors here. And so the ball is going to go up, it's going to come back down. And the first thing you're going to do is measure this height, let's call it h. You're just going to watch from the side and kind of determine where it is and you'll have to use, you'll have to estimate the uncertainty in that height but that's not what I want to talk about. So if I measure just the height, how would I find, how would I find out how fast it was going this initial velocity, v0? Okay, well I know the first thing up here, the velocity I'll call it v2 is zero meters per second. It stopped. So I can say the average velocity, the average equals v2 plus v0 over 2. You can do that if the velocity changes at a constant rate, so the constant acceleration which is what we have here. So that one's zero, so this says v average, this is going to be v0 over 2 and that's going to be delta y over delta t, right, because that's what the average velocity is change in position over change in time. And delta y is, the final y is h, the initial is zero, so this is h over delta t. So I have v0 over 2 equals h over delta t. I don't know the time and I don't want to know the time, that's the whole point. So there's, how can I get the time? Well I can also say the acceleration which is going to be negative g, where g equals 9.8 meters per second squared for a free falling object, is going to be the change in velocity over the change in time. So the final velocity is, say it, zero, right, okay, good job. And the initial velocity is v0, so this is going to be zero minus v0 over delta t. So I can get delta t equals v0 over g. Now I can plug that in down here and I get v0 over 2 equals h over v0 times g, so I get that. And now I want to solve for v0, so I multiply both sides by v0, multiply both sides by 2, I get v0 squared equals 2gh, v0 equals the square root of 2gh. Let me write that over here. So all we have to do is measure h. You can assume g has no uncertainty and then we can determine the initial velocity. Okay, I'm going to erase this out of room to do it another way. Okay, now you're going to shoot it again and instead of measuring the height, you're going to measure the time and it's going to be the easiest, you're going to get the best results if you measure the time to go up and back down. So I'm going to call that whole time up and back down delta t. Also you need to know that the ball thrown in the air has symmetrical motion so that it starts off going v0 up, when it comes back down it has a velocity of v0 going in the negative direction. So the initial velocity is v0, the final velocity is negative v0. Okay, so now let's just use our definition of the acceleration, delta v over delta t, again we're just in one dimension here, the acceleration is negative g, the final velocity is negative v0 minus the initial velocity of v0 over delta t. So I want, so this is equal to g equals to v0 over delta t. So v0 equals one half g delta t, that would be the initial velocity of the ball. So here I just measure delta t and I can determine the initial velocity. I mean one thing you can check back over here, does it have the right units? This is meters per second squared times meters is meters squared per second squared, you take the square root, good. This is meters per second squared times seconds gives meters per second. So now you're all set, you can do the lab.