hi everyone welcome back today we're going to be talking about freely falling objects but what is free fall an object is in free fall if it's subject only to the influence of gravity there's nothing else acting on it just gravity so an example would be this heavy ball and this bunch of feathers that are falling and they are only under the influence of gravity so they are in free fall so an object in free fall experiences an acceleration of about 9.8 meters per second squared straight down and the interesting part is the mass and size of the objects don't matter so in this GIF this is happening in a vacuum chamber so there's no air there's no air resistance or buoyancy to hold these feathers up and make them float down like we know they do so this heavy ball and this bunch of light feathers fall at the same rate and they hit the ground at the same time because they're both falling at 9.8 meters per second squared so in this class we're going to be using 9.81 meters per second squared and it always acts towards the center of the Earth now let's look at some examples of free Falls the most simple one is something that's just dropped and it starts with an initial velocity of zero and it falls like this elephant and I guess this is some sort of coin or other object but regardless of the mass they both fall and they have the same acceleration vectors we can see of 9.8 meters per second squared and they fall and hit the ground the next example would be something having a non-zero initial velocity so this cannon is shooting straight downwards and we know that as an initial speed of 3 meters per second and we can see that our green velocity Vector starts at three and then slowly grows as this object falls and our yellow Vector which is the acceleration stays constant the last type of example we're going to talk about is what I like to call a pop-up that's when something is tossed or thrown straight upwards from the ground and then it goes up and what goes up must come down so our objects as soon as it leaves our hand is only under the influence of gravity so even though it's going upwards we call it free fall so if we want to look at the motion graph of an object with upward initial velocity or pop-up we start with our velocity vector v naught our initial velocity and gravity slowly eats away at it and our velocity vectors shrink a little bit each time until we're left with an object with no velocity that's when it stops and turns around and falls down and instead of being eaten away our velocity is fed by gravity until it hits the ground but this entire time the object is still in free fall now for any object in free fall our position versus time and our velocity versus time graphs will look very similar so for something thrown upwards we're going to have an initial velocity and this position on the y-axis is actually our height and something goes up and then it comes back down and this dotted line right here represents the time at which our object is at our maximum height it doesn't go any higher than right here so now I want you to notice the Symmetry about this line the both sides of this graph are mirror images of each other and that's also true in our acceleration graph now that's much less exciting because our acceleration as we know is constant at 9.8 meters per second squared downwards but at our maximum height here we still have that symmetry on either side this is also true for our velocity graph our velocity starts high up at our initial velocity V naught we know it's positive and then gravity slowly yet consistently eats away that velocity until we reach our maximum height our maximum height is where our velocity is zero because then our velocity becomes negative and it starts falling back down but our graph is still kind of diagonally symmetric right here so now to describe that in a little bit more detail if we throw an object with an initial velocity of 29.4 meters per second then at the end of its Journey it will be going negative 29.4 meters per second the object will have the same speed at every height along its Journey so at 25 meters or one second in five second the object has the same speed of 19 meters per second just one is going up and one is coming down so they have opposite signs so and this will be true at every single point on our graph they have the same speed but different velocities