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AP Physics today we're going to wrap up chapter 2 by discussing section 2.7 Free Fall motion there is a pre lecture Yelp for this section and you can watch it at the mastering physics website  if an object moves under the influence gravity alone and no other forces we call the resulting motion Free Fall any two objects in free-fall regardless of their Mass have the same acceleration Apollo 15 lunar astronaut David Scott performed a classic experiment on the moon taneously dropping a hammer and a feather from the same height both hit the ground at the exact same time something that would not happen what in the atmosphere of the Earth all the earth air resistance is a factor for now we will restrict our attention to situations which air resistance can be ignored  the figure shows the motion diagram for an object that was released from fast and Falls freely the diagram and the graph would be the same for all falling objects regardless of their Mass take a look AA  if you look at the motion diagram it shows at the velocity Vector is down and the acceleration vector is down resulting in increase in speed that you can see by the increasing velocity vectors now look at the corresponding graph it goes with it notice the velocity is in the negative direction and you have a constant acceleration as shown by the slope of the line remember that the slope of a velocity versus time graph indicates the acceleration and the acceleration of this crap is a -9.8 m per second squared  now I have a question for you if we enthrone the up in the air would that ball still be in free fall  the answer is yes when I thrown up in the air it's under the influence of gravity alone when it's at the highest point it's still grab the alone and then when it falls back down it's still gravity alone do not be caught up with the word free fall and assume that an object has to be falling just to be considered in free stop so what would a velocity versus time graph look like if I threw an object up into the air  look hey it is talking about if the object is initially moving up remember the shows the velocity Vector pointing up and when the Vector is an opposite the object is going to slow down but the corresponding velocity versus time graph whatever shape  that looks like that  recall what we learned in the last section at this you have a positive velocity and a negative acceleration because the slope of a velocity versus time graph is negative that imply that the object must be slowing down while this segment looks very similar to what we just craft it shows that you have a negative velocity and a negative acceleration so the bottom section must show that the object is speeding up the we also learned that when a velocity versus time graph crosses the x-axis the object must have a velocity of which applies that the object is changing its direction  so at that point you're at the Apex when the ball was thrown up in the air to the first half of the trip is represented with the first segment and the last part of the trip is the last segment the free-fall acceleration always points no matter what direction the object is moving  the velocity Vector points in the direction that the object moves but a free fall coloration your acceleration is always pointing down because it's a result of the pull of gravity  any object under the influence of gravity only and no other forces is in free-fall and it will then provide us with a free-fall acceleration which is 9.8 meters per second squared vertically downward  by definition the magnitude of G is always positive but you will need to indicate directions with either a positive or A negative when making calculations a falling object beads up because the velocity and Free Fall acceleration are both pointing down likewise and object will slow down when the acceleration Free Fall acceleration and velocity vectors are in opposite directions  because Free Fall is motion with should acceleration we can use the kinematics equations that we learn in the last section for constant acceleration but in the problems you will already know the value of the acceleration due to gravity because it's the value that we just were given G is not called gravity G is called the Free Fall acceleration because of gravity G is equal to 1.8 meters per second squared only on Earth other planets have a different value for the extry fall acceleration due to gravity we will sub X compute acceleration in units of G for example what would be the acceleration in G's of a car of a rocket with an acceleration of  35 meters per second squared how many G's  is this equal to two very easy calculation you'll simply take 35 meters per second in / you're free fall acceleration of 9.8 meters per second squared which would give me the number 3.6 I would say that 3.6 GS  and that's the acceleration  now there is a class video in your textbook does found on page 50 there's a QR code for it you can use your phones and access that and watch that video if you would like take a look at this question what will be the acceleration of a rock thrown straight upward at the it reaches the tippy-top of its trajectory take a second and pause the video and get your answer acceleration due to gravity at this point is 9.8 meters per second squared  down the question not ask what the velocity is at the highest point if I'd ask what the velocity was at the highest point you would have said 0 meters per second remember if an object is accelerating and has a momentary velocity of 0 it must be changing its direction here are some simple facts that are going there was will help you solve problems that are in freefall anytime you have an object is thrown upward remember that the time it takes to reach the highest point has equal to the time it takes to fall back to the original Heights this is because Gravity the force of gravity is what is slowing are the object down on the way up but gravity is also the force that speeds the object back up on the way down and since he doesn't discriminate the time it takes to reach the highest point has to be equal to the time it takes for it to fall back down along the same lines you need to remember that the magnitude of the Velocity now that means it's the numerical number not the direction the magnitude of the Velocity when returning to the original height will be the same as the velocity of the object when it was thrown up I throw a ball up at 30 meters per second when it falls back down to the same height that I threw it at the speed of the I lost you the ball has to be 30 meters per second down that's because gravity will the force of gravity will slow the aab up at the same rate that it speeds it back up on the way down or slow an object down at the same rate that it speeds it back up  Avon but the highest point the velocity is zero but the acceleration is still 9.8 m per second squared down that's where the object changes its direction the remember gravity is the force of gravity is always pulling down on the object even when it's at its high point  Posh Paws do a quick check a ball is tossed straight up in the air at its very highest point instantaneous acceleration is that we know the value but what's the direction pause the video the started when you're ready the correct answer is negative at the highest point the free-fall acceleration is 9.8 meters per second squared down and by convention we usually make the direction down negative take another quick question  an arrow is launched vertically upward it moves straight up to the maximum height then falls to the ground trajectory of the arrow is noted which graph best represents the vertical velocity of the arrow as a function of time ignore Aries the only force acting is gravity  take a minute and get your answer the correct dance D hopefully you recall this earlier we talked about throwing an object up and we actually graph to Velocity versus time graph section represents the arrow slowing down this section represents the arrow speeding up and where it crossed what time access is where it changed its direction  Dulles to a couple problems and then you can start working on your homework a heavy rock is dropped from rest at the top of a cliff and Falls 100 m before hitting the ground how long how long does the rock take to fall to the ground and what is its velocity when it hits the ground notice it's not asking what the velocity is after what's the ground as it hits the ground  first off I want you to realize that we're this problem starts would have been your budget  before taking a look at this I would have started with the object here and then as it falls it's getting farther and farther so your velocity vectors would be getting bigger and remember that you have an acceleration vector that would be down as well which speed it up  and my I guess my pain was so fat sorry it's kind of hard to see that diagram clearly but let's take a look now from it would go along with that motion diagram taking the information out of the problem we would need to realize that The Rock was dropped from rest which would apply that my initial velocity is zero meters per second it also tells us that they Cliff Falls 100m before in the ground so since it's falling we would say our change in position is 100 meters down then it asked what is the velocity right before it hits the ground so that's V2 and it asks that at that point how long does it take the ball to hit that you have to remember here that this object is in free-fall they're not going to remind in the problem that is in free-fall but you have to realize the only Factor affecting this rock is the force of gravity so we're going to realize that the due to gravity is 9.8 meters per second squared  down there is more than way to solve this problem but I'm going to choose first to look for what V2 is right before it hits the ground  and what if I can equations that would work would be V2 squared is equal to V1 squared + 2A  in the what change in X I have all of the values with the exception of the two Sophie 2 squared would it be equal to 0 Plus X in my acceleration being -9.8 since it's down meters per second squared times my displacement was also Stone selex a 100m in make that a negative after I did the math and then took the square root of it my V2 what equal 44 m per second and you have to realize at that point the ball was still moving down that's one of my two answers I'm also asked to find how long this took so I can use V2 review OnePlus at to solve for my time  the two we just found out was 44 meters per second but since it was down we would make that negative is equal to 0 + + -9.8 m per second squared because it was down dogs T which is my unknown and when I would saw for my time here I would get the answer of 4.5 seconds  now you could have actually used the equation displacement is equal to V1 t + 1/2 a t squared + solve for time first and then went back and found your V2 when you get to Point there's often several ways to solve a problem and both or all would be correct  let's take a look at one more example the African antelope known as a spring book Buck would it to me Springbok would occasionally jump straight up into the air a move known as a pronk the speed when leaving the ground can be as high as 7 meters per second if a springbok leaves the ground at 7 m per second hey  how much time will it take to reach its highest point B how much are how long will it stay in the and see when it returns to the Earth how fast will it be moving the first thing we want to do is take the information what a problem and realize that the initial velocity was 7 meters per second in the up  directions we're talking about it a the time that it will take to reach its highest point remember that any time you're at the highest point you actually know the velocity would be so we're going to call V2 which is at the highest point for a 0 meters per second because that's what it changes direction we also realize that this is in free-fall so we're going to know our acceleration due to gravity or Free Fall acceleration is 9 8 meters per second squared in the direction is always down so in a they ask how much time is it going to to reach this highest point the formula I would use here would be V2 is equal to V1 plus a t I know it speed of 0 I know the initial speed was a positive 7 meters per second because it was up plus a negative 9.8 meters per second squared because acceleration was down x t after solving for the time I would get Point setups 37.1 I'm so sorry .71 seconds NB it asks how long will stay in the air now remember those quick facts that I told you when an object is thrown up in the air or lunch is in the air the time that it takes to get to the highest point as to equal the time that it takes to fall back down so if we multiply this number by 2 it'll tell us how long  dr. Antelope was in the air so .71 x 2 will give us a Time 1.4 seconds  and finally and see it asked when it returns to Earth how fast will it be this is another quick answer because if the spring the Springbok actually or something Antelope actually up at 7 meters per second if it reach the same height that now has to be going 7 meters per second but I would have said down as directions or a -7 m per second  one last question is his as she falls faster and faster the air what is happening to her acceleration is it an increasing decreasing or remaining the same now I do need to note since air is underlined we are considering air resistance in this problem pause the video think about it start it back up when you want to hear the correct answer the correct answer is decreases  the skydiver is getting faster and faster but because of air resistance her acceleration is dropping from 9.8 meters per second squared to zero which results in a decreasing acceleration  but she is still accelerating which means she still getting faster and tell her acceleration reaches zero at that point she falls at a constant velocity that is known to skydivers as terminal velocity scraps up chapter 2 and section 2.7 younower assign the 2.7 homework found on the mastering physics website hope this video helps have a great night

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