 Hello, my name is Brad Langdell and I want to talk to you some more about the applications due to gravity Hey, this is part two has all great movies deserve a sequel. Let's take a look at some problems Derek Jeter throws a ball vertically into the air initial velocity of 18.9 meters per second. Hey, there's your initial velocity for this problem It's caught at the same distance above the ground at which it was thrown Which means you didn't like drop it and didn't land on the ground here Jeter doesn't do that He catches it every time now. How high did the ball go? How long was it in the air part a think about the variables? We have an initial velocity of 18.9 meters per second We want to know from starting up here where you throws the ball and goes up to the top of this height Okay, here's Jeter's like hand here something like that where he releases it off the ground. What's this? Displacement, okay, so we're looking for displacement don't know that Well, we do know that when you reach that maximum height the balls got to stop That's the cool things that go up a cool thing about things that go up eventually they stop That means it's final velocity in the motion that we're concerned with is zero meters per second So it means my final velocity is zero and of course as always we know the acceleration due to gravity is negative 9.8 1 meters per second squared. Okay, what do we got for formula this here? Well, we could use Vf squared equals vi squared plus 2ad You can substitute in we know that the final velocity is zero 18.9 meters per second square that plus 2 times negative 9.8 1 meters per second squared times the dm what can four all right? So we're gonna run through the old calculator see what we get here I'm gonna go and take my 18.9 I'm gonna square it All right now I'm gonna move that term to the other side all right I'm gonna move that to the other side by subtracting whatever that number was 357.21 From both sides and move it to the other side. So it's gonna be a negative all right There it is on my calculator I got a negative value and I'm gonna divide it by 2 and I'm gonna divide it by negative 9.8 1 This thing is gonna go 18.2 meters up into the air Not bad not bad Okay, now how long is it in the air for okay now? We're asking for time So we've got time to throw into the mix we can use a lot of the information for the last question though But the problem is when we want to know how long a ball is in the air for we're not only concerned with its initial Velocity when it's thrown up at 18.2 meters or 18.90 meters per second We also want to know how long does it take to come back down now? Here's the cool thing about motion kids and gravity when you go up at 18.9 meters per second that ball will come down at negative 18.9 meters per second They are the same but one's negative if it's coming down So that means we can use that to help solve this problem to solve for time In fact, we can do it really easily just using the accelerated motion formula definition of acceleration Final vibe minus initial velocity divided by time So I have acceleration negative 9.81 meters per second squared I got myself a final velocity. I'll be careful here negative 18.9 meters per second is the speed it comes down with We got to get that negative in there minus Positive 18.9 meters per second. I'm being careful to put my integers in divide by time So I'm gonna go through here. I'm gonna substitute everything in I'm gonna go and divide Negative 9.81. I know I'm going to do my subtraction first negative 18.9 minus 18.9 and now I'm gonna go through and divide by negative 9.81 So that ball is in the air for a total of 3.85 seconds And you know what if you wanted another approach of doing that You could definitely figure out how long it takes to go from an initial velocity of 18.9 to a final of zero And that's going to be half the time that I gave you down here Or you could say how long does it take to go from initial to final of negative 18.9 same formula But by giving it different final velocities it spits out different time So try that one out and there's more problems like this on the website www.ldindustries.ca