(host) This is a wrecking ball dropped by the guys from the YouTube channel How Ridiculous, falling from a tower 35 meters above the world's strongest trampoline. You might think the most interesting part is waiting to see if the ball smashes through the trampoline, which it does not. But you're wrong. The most interesting part is that we can figure out how long it took the ball to fall. Meaning, if you got to jump on a trampoline from that high, how much time would you get in thrilling freefall? Hello! Whoa, I scared myself. Hello and welcome to lesson 2 of Dianna's Intro Physics class, also known as AP Physics 1 review, also known as Physics by Dianna. I still don't have a decent name for this class. Anyways, today's lesson objects in freefall. Today's theme Tom Petty.

(Describer) She wears shades and strums a guitar.

If you don't know who that is, you're not alone, but he sang a song called Free Fallin' which I can't play because copyright. So free fall--objects falling down, objects falling up; that's today. Last lesson, we developed some simple modeling tools, and today we're going to use them. And we're going to look at mathematically how your position and your velocity change as you fall. That's how we're going to understand freefall by the end of today. Forget wrecking balls and Tom Petty for a minute, and recall the very strange moment in internet history.

(Describer) A water bottle falls on her table.

Oh, it's so close.

(Describer) She repeatedly tries flipping the bottle so it lands upright.

It's hard.

(Describer) She succeeds.

The bottle flipping challenge. Now I get why everyone's so excited when they finally get it because there's, like, 50 takes you don't see. Bet you didn't know that this challenge has an excellent physics riddle built in. Here's the riddle for you. Have a water bottle and I throw it in the air from the height of the table and then it lands on the table. What takes longer, the trip up or the trip down? Let's simplify the question. Let's say that I throw it and then catch it. So I throw it from the same height that I catch it--from the height of the table. Throw it up, it falls down and then I catch it at the same height. What takes longer trip up or trip down? Spoiler alert. It's actually a double trick question, and we're going to answer it using the tools from our first lesson. So what do you think longer on the way up or longer on the way down? Ask some friends, and you'll get all sorts of answers. A common response is, "gravity is working "against you on the way up and gravity is helping you on the way down." So clearly the trip on the way down is faster. Super common response, but there is a deep problem with it. Can you see it? Let's think it through. I'm going to start with the bottle going down, and it's time for some excellent drawings. What I'm going to do throughout this whole next section is I'm going to look at snapshots of the velocity of the bottle on the way up and on the way down to figure out which took longer. And along the way we're going to learn a lot about how to analyze time, velocity, and acceleration in freefall.

(Describer) She catches a thrown marker.

[fanfare]

Forget that I threw the bottle; imagine that I was standing on the top of a roof,

(Describer) She draws.

and I just dropped the bottle. What happens? Let's look at snapshots of the bottle on the way down. Instant you drop it, we'll label time--t equals 0. What is its velocity there? It's zero, we just dropped it. What's it's acceleration? Well, near Earth's surface, acceleration due to gravity is about 9.81 meters per second squared down, but today we're going to round up to 10. We're playing very fast and loose with significant figures today, but I promise you and your physics teacher, we will worry about sig figs when we need to. I'm also going to suck all of the air out of my scenario and completely neglect air resistance. So acceleration is roughly 10 meters per second squared, but the bottle's instantaneous velocity is 0. That's kind of weird to think about. Its velocity is 0 but it's accelerating right away. It only starts to fall after 0.000000-- however many zeros you can pack in there, zero, zero, zero, zero, zero, one seconds. That's cool. Let's take a look at one second later. T equals 1. How fast is it going? It has fallen for 1 second with an acceleration of 10 meters per second per second. So it's velocity is 10 meters per second. What's its acceleration now? Well, it's still near Earth's surface, so it's still about 10 meters per second squared down. How far has it gone? Let's think about it for a second without any fancy equations. If the bottle started at velocity 0 and it fell for a second, and ended

(Describer) On a graph...

at a velocity of 10 meters per second, falling at a constant acceleration, than its average velocity is-- sorry, this is 10. Then its average velocity is 5 meters per second. So average velocity is 5 meters per second down. Now finding the distance I fell in that first second is easy. Falling for 1 second at a rate of 5 meters per second on average. So it has gone 5 meters in a second-- 5 meters per second, which is also the area under my v versus t graph. Easy. This is a simple, very useful trick to find the average velocity, and I'll use that for distance. No formulas; just basic definitions and thinking about what's going on. We'll call this the average velocity trick, and we're going to keep using it. Like probably for the rest of this course. Probably. Don't quote me on that. One more second later, t equals 2. How fast is it going? Well, the acceleration is still the same-- a equals 10 meters per second squared down. So I gained an additional 10 meters per second. So I'm now going 20 meters per second down. T equals 2; it's falling now at 20 meters per second. So how far has the bottle gone? Let's use the average velocity trick and look between t equals 1 and t equals 2. The bottle started at 10 meters per second and it ended at 20 meters per second, which means it's average velocity, halfway between, is 15 meters per second down. So in 1 second, it went 15 meters, which is 10 more meters than it went last time. So it's change in position is 15. The bottle has already gone 5, so now it's position is 20--

(Describer) She writes 20, down from the original position.

20 meters. Right here it was 5 meters. Oops, this should be down here. A feature of the building... 20 meters.

(Describer) She writes it lower.

This is the position; this is just the distance it's traveling between. Let's look at the next second. T equals 3. That's another 10 meters per second added to the velocity. It's accelerated at 10 meters per second squared for another second, assuming it hasn't hit your face yet. And to find the average velocity, I use the average velocity trick again between 20 and 30. Between time t equals 2 and 3, I went an average of 25 meters per second down. So what's the change in position? I went an average of 25 meters per second for one second, so I went 25 meters. So then my position here, now, is 20 plus 25. I'm at right here-- 45 meters. So you already see something pretty cool. It fell farther every second because it's accelerating. This is exactly what you see if you measure even time intervals of anything falling, if air resistance is negligible. So we just calculated it'll take the bottle 3 seconds to fall 45 meters when it is accelerating at 10 meters per second squared. So we're done with the falling part of the bottle. We're going to have some really interesting questions about freefall in a minute. But first, I want to see how the bottle moved on the way up.

(Describer) She moves her sheet of paper to a blank area.

I don't need to pretend that I'm on a roof anymore. So our starting position, y equals 0. I'm going to throw the bottle up right at t equals 0, with an initial velocity of-- I'm just going to say 30 meters per second. That is the same as the final speed on the way down, which seems like a pretty good assumption. And we'll get a reality check on that in a minute. My acceleration is still 10 meters per second down. It is that throughout the entire trip whether you're going up or going down. After 1 second, gravity is pulling down with the same 10 meter per second squared against this motion. So my velocity, I lose 10 meters per second in that 1 second. So my velocity is now 20 meters per second. So that initial guess that everyone has that gravity is working against you is true. Gravity is now slowing the bottle down instead of speeding it up. Now you'll start to see something familiar. The bottle's average velocity was 25 meters per second. Imagine the bottle is actually up here right now for t equals 1 second. I did this wrong. OK. This is a big old bird right here. It's not a bottle, and it didn't get hit by the bottle; don't worry. T equals 1 second is actually here because my change in position here, I went 25 meters per second for 1 second. So this should actually be 25 meters here. This is all up here.

(Describer) She re-writes the new position higher.

Everything still stands. I just wanted to draw this up here so you could see that we went 25 meters. Now my position is y equals 25. And now we do the same calculations as before for the next second of flight after 2 seconds. T equals 2. It will have slowed down to 10 meters a second. And you can see where this is going already. The average velocity is now 15 meters a second between these two times and I did it for 1 second, so that my change in position is 15 meters. And now position is 25 plus 15, 40 meters in the air. Now in the last second, t equals 3-- the bottle slows down from 10 to 0. In the last second, my average velocity, halfway between, is 5. So the bottle went 5 meters. So my position is now 45 meters. The trip up is exactly symmetric to the trip down-- 5, 15, 25, 5, 15, 25. This may have been intuitive to you, so pat yourself on the back if it was, because it's not intuitive to a lot of people at first. The only difference is the direction of the velocity. On the trip up, your velocity is this direction, and on the trip down, your velocity is this direction. So which takes longer, trip up or trip down? With no air resistance, it's the same. The time up is the time down. You'll hear me talk in the next video about projectile motion and about time up and time down and how they work out to be symmetrical. This is part 1 of our trick question, though. We've just shown that time up and down are the same, but it gets trickier with the little thing called air. And so we're going to come back to that at the very end of the lesson. OK. Cool. We could have done this, though, with that cool tool we introduced in our last lesson--the basic equation of motion in 1D. Let's use this tool to solve the wrecking ball problem and then what about diving into a pool?

(speaker) One. Yes!

(Describer) Again, the wrecking ball is released and falls onto the trampoline.

We're away. We're away. Me load?

(Describer) Bouncing up, it comes back down.

Oh! Yes! So starting with the wrecking ball, the question is, if we drop the wrecking ball from 35 meters up, how long should it take to fall? We can do this fast. Start with our equation of motion. This is our mathematical model of how things move while accelerating.

(describer) Y=Y sub 0 plus V sub 0

(Describer) y equals y-sub-naught plus v-sub-naught t plus one-half AT-squared.

t plus 1/2 a t squared.

(Dianna) But today we're using y instead of x because we're talking about up and down, and it just makes sense to use y when talking about vertical motion. But we use this to find how long, t, it took something to fall some distance. We're dropping the wrecking ball from rest,

(Describer) Y.

so my initial velocity is 0.

(Describer) v-sub-naught.

So this term is 0.

(Describer) She crosses it out.

And we're just going to set the initial position to be 0.

(Describer) y-sub-naught.

So this term goes away. Boom, simple. Now I have a really nifty equation, y equals 1/2 a t squared, which is really fun to have in my pocket. The distance the thing will fall is half the acceleration times the time, times the fall time, squared. Since we're near Earth, we'll always accelerate at 9.81 meters per second squared down, which we will round up to 10. And a lot of times, I won't use y, I'll use d, because this is a pretty famous tool. D equals 1/2 a t squared. It's even fun to say: d equals 1/2 a t squared. And I use this if I have no initial velocity and I start with my position at 0. Then my distance traveled is 1/2 a t squared. OK, our ball. Our ball is about 35 meters above the trampoline. My acceleration is 10. And you'll notice I'm ignoring this sign because we know it's down. We'll just keep that in our heads and we'll solve for t. So d equals 1/2 a t squared. Our d is distance, 35... is 1/2 times 10 times t squared. Bring the 2 up, bring the 10 down, 70 over 10 equals t squared. I'm ignoring the units, but you can keep track of them. And our t is the square root of 7, which is a little over 2.6 seconds. There it is. Now check this out. Let's go again! Three, two, one!

(Describer) In the video...

(Describer) The man on the tower drops the ball and it bounces on the trampoline.

Yes!

(speaker) We're away, we're away.

(speaker 2) Me load? Oh! Yes! And again, and again.

(Describer) The ball lands in sand around the trampoline.

Oh let's go. Yeah! How high did it bounce? She went, Gaunson! She really went high. I love it how he wants like a distinct measurement and you give him, "She went high." How far up did it bounce? Well we can figure it out now. Taking a frame by frame look, we measured that it took the ball a little over 1.7 seconds to rise back up to the top of its flight before it started falling again. Let's use the same tool. D equals 1/2 a t squared. But in this case, we have t and not d. So d equals 1/2, acceleration is 10, t squared, t is 1.7. So 1.7 squared and, you know, we'll use 9.8,

(Describer) T is the time back up.

just for fun for the acceleration. And we get just over 14 meters. So yeah, it went. This is on the way back up.

(Describer) She writes, "Wow!"

(crowd) Ahhh! Now how fast do you think it is going right when it left the trampoline heading up? Well, I can tell you right now. About 17 meters per second. Let's think about it. It flew up for 1.7 seconds, so gravity had 1.7 seconds to slow it down at a rate of 10 meters per second every second. It's 10 meters per second slowing it down for 1.7 seconds. So that's 10 times 1.7, 17 meters per second. So think you can see what we're doing here. We're thinking about up and down motion problems as simply as we can using average velocity and d equals 1/2 a t squared wherever we can to keep it simple. But let's try another problem, a little bit harder. This one would be maybe the AP Physics level problem you might see. All right.

(Describer) She moves the paper again.

Standing on a diving board.

(Describer) She draws a stick figure on a board above a pool.

It is 5 meters up from the pool. I'm going to hit the water and I measure that it takes me 2 1/2 meters, probably, in the water to stop. There is a reason that pools are deep. Now my acceleration as I'm falling towards the water is 10 meters per second squared. Here's the question. What is my acceleration while I'm in the water? This looks hard, but let's take it step by step. If I want to know why acceleration in the water, I need to find my speed when I first hit the water. And let's do that by analyzing the top half of this problem first, which is: If I jump from a height of 5 meters, how fast will I be going at the end of those 5 meters? I need to find out how long it takes to fall. I need the time. But we're practiced at this a bunch. D equals 1/2 a t squared. I know my d is 5, equals 1/2 times 10 t squared. I can solve for t, at 2 up, 10 down;

(Describer) Two times five, over ten, equals 1 for t-squared.

2 times 5 is 10 t squared. So my t equals 1 second. Look at that, it takes 1 second to fall 5 meters. So the whole problem becomes simple because my average speed is 5 meters in 1 second-- 5 meters per second. So now I can use the average velocity trick backwards. If I started at 0 and my average was 5, then I ended at 10 meters per second. I'll just call it V0. V0 here. V0 right when I had the water. V0 equals 10 meters per second. So now I'm going to use d equals 1/2 a t squared again to find my acceleration in the water. I know my distance is 2.5 meters, and to find my acceleration, 1/2 a t squared. To find my acceleration, I need to know the time it took me to decelerate from 10 meters per second down to 0, to where I stopped. But I already know how long it took me because I know my average velocity. I went from 10 to 0. So my average velocity is the same, 5 meters per second. Same, same. Same 5 meters per second. But I traveled at that speed for 2.5 meters this time. Half the distance. So I'm getting tricksy. It took me half the time. So this time my time is 0.5 seconds. So this is 0.5, this t is 0.5. So 2.5 times 2 equal over 0.5 squared equals a. If I'm dividing by 0.25, I'm actually multiplying with 4. I've got 2.5 times 2, which is 5, times 4 is 20. My acceleration then is 20 meters per second squared. And voila! That is about 2 Gs. It's about twice the acceleration you would feel due to gravity. Interestingly, I went up in the Vomit Comet, which is this plane that takes you up and it makes you experience zero gravity. But before you experience weightlessness, the plane pulls up and you feel 2 Gs. You feel twice gravity. It's crazy because you feel twice as heavy as you normally do, and it's almost impossible to stand there; they make you lie down. So 2 Gs, it's no joke. It seemed like a hard problem, but we were able to solve it with all the tricks we've learned. And now we can go back to our original question. Remember, we asked, if I throw a bottle up in the air, will it take longer on the trip up or the trip down. And we neglected air resistance because air resistance is way beyond Intro Physics 101. But we can think about the simple idea that air resistance slows things down always. On the way up our bottle starts at a high speed

(Describer) She draws.

and it ends at 0. And on the way down--"up." And on the way down, it starts at 0 and it ends at high speed. So say in the middle of the half, like here, gravity is pulling it down, slowing it down. Here, gravity is pulling you down, speeding you up. And with no air resistance, gravity slows you down on the way up just as much as it speeds you up on the way down. Here air resistance slows you down with gravity. Those should be the same direction. Slows you down with gravity because it's opposing your motion. Here, air resistance slows you down against gravity. You're slowing down faster then you're speeding up. So you're slowing down faster. You're getting to 0 faster than you're getting from 0 to your speed down here because the air resistance is acting against gravity here. So you'll spend more time hanging out here on the way down. If you hit a balloon up in the air, this question becomes a lot more obvious. You can see it goes really quickly on the way up, and falls slowly back down. This is one of the common ways of answering tricky questions in physics. You take it to the extreme. In this case, try answering the question with a really low-density object. I know this is confusing but if you're not convinced, then we will get to lecture 9 where we'll answer the question again using energy, and you will be 100% convinced. That's our second lesson on free fall, and, when they ask you what you learned on YouTube today, here are your two important takeaways. If you throw a bottle up, the trip up is symmetrical to the trip down without air resistance. And, remember, the average velocity trick or use the handy tool d equals 1/2 a t squared. Now we just touched on the basics of freefall, which seems so Tom Petty.

(Describer) She puts on the shades.

But did you know physicists are working on an experiment to drop antimatter? If you haven't heard of antimatter yet, oh, you are so lucky right now. There's this type of stuff that's kind of the opposite of matter. And if matter and antimatter come together, then they annihilate, which is the very simplified version of what antimatter is. And at this massive crazy science facility in Switzerland called the Large Hadron Collider, physicists are working on experiments to drop anti-hydrogen. That's the whole experiment. They want to see whether it falls up or down. They think it will fall down, but if it so happens that antimatter does fall up, well, that would shake up the whole field of physics. If you continue on with physics and take a class in particle physics, you'll learn about antimatter and a whole lot more. I hope you do continue with physics. And because you can only really learn physics by doing the problems, here again are all the problems we did in the lesson. And you should definitely go work them again at home.

(describer) Problem one: If we drop a wrecking ball

(Describer) Problem 1: If we drop a wrecking ball from a height of 35 meters, how long will it take to fall? Problem 2: The ball bounces on a trampoline. It takes 1.7 seconds to reach its maximum height. What is the height? How fast was the ball going when it left the trampoline? Problem 3: You dive off a diving board, 5 meters high, into a pool. You end up 2.5 meters deep in the pool. Assuming constant acceleration, what was your acceleration while the pool water was slowing you down?

from a height of 35 meters, how long will it take to fall? Problem two: The ball bounces on a trampoline. It takes the ball 1.7 seconds to reach its maximum height. What is the height? How fast was the ball going when it left the trampoline? Problem three: You dive off a diving board, 5 meters high, into a pool. You end up 2.5 meters deep in the pool. Assuming constant acceleration, what was your acceleration while the pool water was slowing you down? And now a special message for you from a special guest. Hey, everyone. Nice to see you here. I am Dr. Daniella Bardalez Gagliuffi. I am an astrophysicist from Peru, and I work at the American Museum of Natural History in New York City. I study brown dwarfs, which are stellar objects with intermediate mass and properties between Jupiter and other small red dwarf stars. What you just learned today about freefall and motion is the basis of what I use for studying the motions of stars. So I hope you keep learning physics and one day maybe become an astrophysicist too.

[music]

(Describer) Titles: Executive Producer/Host/Writer: Dianna Cowern Lead Writer/Course Designer: Jeff Brock Producer: Laura Chernikoff Video Editor: Victoria C. Page Researcher/Editor: Sophia Chen Videographer: Levi Butner Curriculum Consultants: Lucy Brock and Samantha Ward Transcription: Alicia Cowern Physics Girl Accessibility provided by the US Department of Education.

Accessibility provided by the U.S. Department of Education.