So I'm going to add those two vector, velocities together okay so if I say and for that one remember the gravitational velocity is going to be a negative value whereas my initial velocity up is going to be a positive value. So how do those two distances because my velocity going up is going to start at 20 my velocity due to gravity is going to start at zero and then it's going to slowly increase, it's going to continue to increase.

How high will it go in the air okay, well now I want to figure out the distances and again distances for velocity is velocity times time, distances due to the force of gravity is one half gravity times time squared okay. So that answers part one, now let's look at number two. Now if I'm asked how long will it remain in the air total, well that's going to be 2 seconds up and 2 seconds down okay. So my ball is going to stay in the air for about 2 seconds okay, before it starts to come done. I can see that my t equals 2 seconds okay. Pretty easy problem, if I see the 20 meters per second equals 10 meters per second times t I can see that seconds squared and this is going to be unit in seconds so they'll cancel. So my initial velocity is 20 meters per second and I want to know at what point will that equal 10 meters per second squared times t okay. That'll be close enough for our calculations here okay so I want to know at what point will my initial velocity equal the velocity due to gravity. And to solve problems like this it's useful to simplify, so let's simplify that to 10 meters per second squared.

And again the force of gravity is 9.8 meters per second squared. The difference due to gravity is 1 half gravity times time squared, that'll be useful for the second part here okay. Okay, well again to solve that let's look at a couple of equations okay first off the distance traveled due to a simple velocity is just a velocity times time, so meters per seconds over seconds okay. So now it's at the point at which its velocity due to gravity has equaled to velocity due to the initial velocity applied to the ball. So let's first look at linear motion, again simply put it's just change is distance over the change in time okay.Ī problem you might see related to linear motion is a ball thrown straight up at 20 meters per second for how long will that ball move up and how high will it go? How far will it travel? Okay to solve that we need to think about it so, we're throwing the ball up at 20 meters per second and it's going to up until the velocity due to gravity is also 20 meters per second. That's a little different than parabolic motion where it's moving at an angle and the force of gravity is also pulling it down. Let's talk about linear motion, here's an example of linear motion I take this tennis ball and I throw it up and down it's moving in one dimension okay.

Linear motion