all right hey welcome we're going to do lab number three and lab number three is a projectile motion and it's really kind of a a fun lab it's really fun in person so uh the in-person class just got done they had a good time doing it here so let's see how ours comes out and again like all of these labs you know all be the person who does the hands-on thing and you'll be the person who does some calculations and does the thinking and ultimately turns in the lab assignment and ultimately gets gets a grade here so let's talk about projectile motion kind of in review here let's say i have an object and i'll start with it right here and i'll just make a little round object the reason being is for our lab here we're going to shoot this little yellow ball across the room okay a couple times actually and so this will be my starting point uh the ball will get launched up at some initial velocity and some angle theta it's going to go across the room and since we're shooting it from up on a table it's going to then land on the lab floor which is going to be lower than where it starts now as you heard me say quite a few times when you do these calculations make sure that you make it clear in your mind where you're going to put the origin now the little lab instructions that i sent you with this video have this is the front page and then some more stuff on the back so that's coming up but on this page they go through the mathematical derivation and i'll just note that your author picked the launching point as the origin so i'm going to follow suit with that you can vary it if you want but i would encourage you not to for today's lab to call this the launch point because if you then go to do some calculations and you put x and y like we've been learning with our projectile motion you can say that the initial position in the x direction is zero and also the initial position in the y is zero okay now also as you've seen us do a number of times we can take the velocity initial and the angle and make the x component maybe i'll put it over here on the side since we've done this quite a bit i'm guessing that you're getting pretty good at it and that the x component then would be the cosine function and for the sine function we would get the vertical speed so moving v naught over to the other side of the equation we can say up here that the initial velocity in the x direction is the initial velocity cosine theta and initial velocity in the y direction is the total initial velocity times sine theta and so that's kind of our standard projectile motion and that's what this lab is about is to give you some experience some more experience working with projectile motion now the other thing we know since it's a projectile and it's under the effect of gravity we know the accelerations maybe i should put that in here too so the acceleration in the x direction is zero and the acceleration in the y direction is negative nine 9.8 meters per second squared and so if we apply the equation x equals x naught plus v naught x t plus one half a x t squared starting with the idea that the acceleration is zero so that term goes away the initial position is zero so that term goes away we have x equals v naught cosine theta t and that maybe i'll put a little circle around uh to say is the mathematical equation representing the position of the flying objects at any moment in time given the firing angle and the initial velocity doing that same logic here would be y equals two y naught plus initial velocity y times t plus one half a y t squared so in our case only one of them is zero for the for the y direction and so we would get y equals and here i can put v y sine theta t and then over here i can put a minus 4.9 that's what happens when i put the one half together with the negative 9.8 and then a t squared okay and uh let me uh let me run says i'll put the units here real small but i don't i don't want to put them in our calculations because we're gonna have a quadratic and it's probably better without the units in the calculations okay oh and let me put a little circle around that because that's the general idea of projectile motion let's look at what we're asked to do first and so taking the lab manual here and or lab sheet and turning it over to the back side here it says this step one determine the initial velocity of the projectile when you fire it horizontally that is theta equals zero okay so i should probably show you the equipment here's the equipment it's this little spring loaded cannon uh you put the ball in there you push it in [Music] and when you pull the release string it fires and in this case it just shot it across the room there and so this is what is called our canning it's a little spring-loaded cannon and i'm gonna change the angle just a little bit so that i hit more of the door and i'll kind of show you again and of all the labs this is the funnest one to do in person i gotta say this is fun just to pull this and watch it fly across the room in this case i'm hitting the door and it's bouncing off here so this is our canon and remember what i just read about the procedure it says first fire it at zero degrees so i have some wingnuts over here on the side that will allow me to change my canon and i have a plum bob on the side that allows me to measure this angle and i think i'm at zero degrees i'm going to come over to this side so i can see it a little better yep zero degrees so i've done what they've asked which is to set up my canon at zero degrees and then it says find the initial velocity well how's that going to work well watch this if you come over here and set the angle at zero degrees and then you fire it and see where it lands we can then measure how far horizontally did it go and how far vertically did it drop and if you look closely then if you know these three things and you come over to this equation you can put in sine of zero which hopefully is easy for you that's zero so that term goes away and then if you also put in the y value that you measured you're going to have an equation here that only has time so you could then use the vertical equation to calculate the time it is in the air and then kind of like our homework problems once you get the time you can use that over here in this equation and so if i put time in here and remember the angle is zero and so i'll just remind you that cosine of zero is one and then we got the x because we're going to measure how far it goes we can then solve for what they've asked the knot and so that's the the strategy and so since i'm your hands to make the measurements i'm going to measure this and set up the canon for this and then i'm going to actually pause it and say you need to calculate the time and the initial velocity and i'll even do the calculations myself and so when i unpause the video camera i'm going to have an answer but hopefully you will have an answer first and hopefully our answers will agree okay to find out how fast does this little cannon shoot and that's step one so without reading further down on the procedure let me actually measure these and and here's how we're going to do it uh the first one's pretty easy and that's the the vertical because i'm going to fire it here horizontally and it's going to go across the floor and our floor is roughly and i'll say roughly horizontal so i'm going to assume that the distance from down here to the floor is the same as what it falls although our room does have a little slope all labs do because we put a little drain over there in case something goes wrong so unlike a house we don't want a level floor we want a slope to it and but the drain is far enough away that i we're going to take that as negligible okay so i have myself a two meter stick and again i'm your hands here so i'm going to place the two meter stick with zero on the ground and then measure up to the bottom of the ball and they have a little plastic mark right here so it looks like it's 116 centimeters and i don't know because of this plastic piece if i can do any better and i don't know if that's level but actually it looks like it is a little more i'll call it 116.3 okay now the 116 is centimeters so let me change that to meters so 1.163 meters careful it lands at a negative distance maybe this is worth looking at the pitcher over here right i've technically just measured up 1.163 meters but this equation means where is the position of the ball [Music] in reference to zero so picking zero as the launch point and noting that it lands below where it started i would then say it needs to be a negative and when you go to do the math that's real important because if you don't put a negative here later on you're going to try to take a square root and you'll be trying to take the square root of a negative number and you'll be going that i can't do that something went wrong yep something did go wrong and there's a lot of things that can go wrong but this is an easy one to overlook not putting the negative for the y now the x is a little harder to measure because we actually have to fire it and see where it lands and so i've got a little technique for that uh my technique starts with this it starts with me firing it the first time to get a rough idea because the second time i'm going to put something that i can measure it better with now to help me i'm going to grab a piece of paper and i'm just going to put the paper roughly on the grounds i have no idea if i will hit that paper but at least once i shoot it i'll be able to then say oh i need to move the paper because i want the ball to land on the paper okay and so this will just give me a rough idea so i'm going to guess that it's right about there i'm going to just kind of eyeball to make sure the paper is straight down the spine of my cannon and it sort of is maybe i'll move it a little bit more and i don't know ron if you want to watch from here or put the video camera down where it lands whatever you think is best uh maybe you'll shine it at the paper so they can kind of see it and i'll just count you guys can hear me release it on three one two three fire ah so i hope what you guys saw is that it landed just a little beyond the paper right about here so i'm going to kind of put that in the middle of the paper thinking now when i shoot it it's going to hit the paper in fact i'm so confident that it will hit the paper that i'm going to just tape the paper on the ground so that when i measure distances it uh won't move and i'm also going to play a little gain here or trick by putting what is referred to as carbon paper and what it is is this black paper and i'll put another sheet right here and if i bounce the ball on it you'll see that the impact of the ball leaves a little smudge and so i don't need that piece of paper but what i'm hoping it happens here is that i will hit the carbon paper and it'll leave a smudge so i know where it landed and then i can carefully measure the horizontal distance and so that's how we're going to measure this together oh keep bumping this my sound still good one once you double check that yeah i suppose you should check to make sure the camera is still working oh can you hear me sounds good all right all right so yeah point it at me for just a second so they can see me load it but now we're actually ready to make the measurement so i'm going to load it up i'll double check that the angle is zero sometimes me bumping it around can change but that still looks good at zero i'll double check that it's still straight down the the spine that looks good okay and i suppose ron why don't you point it at the paper maybe they'll see it go i don't know which is better to see and on the count of three i'll shoot it and hopefully it'll skip off that uh carbon paper and leave a smudge one two three oh i barely hit it i wonder if i messed it up but i think it did get the edge of it oh right there is it really cool yeah so there's a smudge do you think i should shoot it again all right maybe i'll move the paper over a hair i wonder if i bumped it when i pulled it oh yeah you know i don't think my clamp's very tight let me okay all right all good well we get a fire another time because this is kind of fun anyway so maybe we should miss it a couple of times all right so let me load it up let me look at zero let me look down the spine let me try to be a little more careful when i pull it so i don't twist it on the count of three one two three ah there we go and so now i bet you can see the little smudge right there okay and so there's the smudge mark and so now let me measure how far that is all right so remember this big long two meter stick i'm going to place this 2 meter stick kind of near the ground but i'm going to take advantage of a few short measurements here it looks like the ball gets launched at about two centimeters back from this edge and this edge is at the edge of the table and this lip hangs over by about two centimeters and so i would say that if i put the zero of the two meter sticks straight down from the edge of this wood it would be right over that lip which is right where the ball gets launched and who knows maybe i'm off by a centimeter or or so okay so it went a pretty good distance and i need a that looks pretty good go right towards that that smudge okay uh no no ron was asking me normally i have the students tape it because there's so many other people walking around but right now we don't have that it's just me doing the experiment so i'll just kind of tap this here and you'll see then that this must be three meters and that would be 3.2 and we're just shy of 3.3 maybe i'll take the kind of the center of that smudge so 3.2 nine four two nine four and i better write that down right away two nine four two nine four ah and so 3.294 meters just shy of 3.3 all right well we're only on step one but this is going to be a good place for our first stop and let you guys do some work now and i'm going to say this that i've measured the x and the y and set up the angle so you know these three use these equations that i talked about and calculate the time and then calculate the initial velocity and then we will have accomplished one all right see you in a second bye now all right so now i've unpaused it i hope you took the time to do that because i did it's right here i'm kind of hiding it from you but i am going to give you a little bit of hint i first calculated the time using this equation and i got a number that's a little bit under a half a second okay and you should have two then once i got that time remember i put it into this equation and i got what this was asking for the initial speed and i got a speed that is under seven but more than six and a half okay and so again maybe i won't tell you the exact speed but i want you to go through those calculations because you're going to need those moving forward or actually you only need one of them you need the initial speed because here's our thinking our thinking is if we were to change the angle on that cannon we're going to assume it still fires at that same speed so this was the point of calculating the initial speed when we fired horizontally hoping then if we change the angle it would still fire and it at the same speed and and it does that pretty good it's not perfect but it's pretty good so let's use that to our advantage watch let's let's keep going on here all right so now that i wrote down these answers let's go to step two step two says set up your cannon to fire at an angle greater than 45 degrees okay so i'm going to kind of loosen this up a little bit and give it an angle and about there kind of a lob i'm so going to go up in the air but if you remember before we actually started doing this i was hitting the wall so i want to give it a little more of a lob oh i don't want to hit the ceiling i i think we'll be okay i don't think we're gonna hit the ceiling okay because i in the past i know i hit the ceiling if i go more than 70 degrees and i'm a hair under 60 i'll measure it more more accurate all right all right so i did step two without you with us step three here's the fun part it says measure your angle and then calculate how far this should go horizontally all right let me start setting up a table here because my table is essentially the same remember the first time i i set it up at theta equaling zero so this time i'm going to set it up at theta equaling 59 degrees and maybe i'll even just tighten it up a little bit so it doesn't move on me let me just check still at 59 okay so we have a pretty good angle here 59 degrees and i would say that we know a couple of things as we fire this cannon first of all we know the why now it might be hard to tell on the video camera but when this cannon pivots like i did and i don't want to touch it too much it pivoted right where the ball gets launched so it did not raise or lower the ball the ball is still being fired right there oh lost the ball oh i really lost it oh one way over here okay so you are to no huh oh yeah i better check see if i bumped it off of 59 thank you yep still at 50 still 59. but what i'm trying to say then is for this calculation we know that even though it's going to lob up pretty high it's going to fall back down and land somewhere over here on the floor and so its final position is going to be that negative 1.163 meters okay now the firing velocity is i'm just going to put the same this was really the whole reason of doing this first step was to find that number and it won't be perfectly like that but we're going to assume it is and see what happens and so okay now when i fire it a second time we're going to say it still fires at that same speed okay even though it's kind of angled up a little bit it's got to fight gravity a little bit but for the most part it'll be that that same so we then know these what could we calculate and i claim coming back to this equation that if i look at it let's see i know the y i know the initial speed i know the angle i know everything in here but time i can solve for time now be careful because remember i said when you were firing at zero degrees we calculated a time and it was under a half a second but it's not the same amount of time now now we're lobbied it up and so i expect the time over here in this calculation to be quite a bit bigger okay much more than a half a second but of course what workout we're asked to calculate is where it will land where the x is and so that's going to be your assignment and i'm going to hit pause here on the video camera and have you hit pause and say okay now what i want you to do is to sit down and do a calculation first calculating the time and then calculating how far it will go and i'll do the same thing okay and so over here i will tell you that if you use the y motion to calculate time again and then put it into here you will get how far this should go so it's kind of like a like a homework problem and so go ahead and hit pause and i'll hit pause and i'll do a calculation and then come back alright see you in a second okay well welcome back i i hope you took the time to do the calculations i know i did and they're right there and so this calculation for time and so as i said i put in this information into this calculation and this is probably the hardest step here of the lab and an important one for you to do is to make sure you can solve a quadratic equation and so it is a quadratic and you get a time of and i won't tell you the exact number but i will tell you that because it's quadratic there's two answers and one is a positive and one is a negative uh i'll show you in the picture but you want the positive one not the the negative one in fact coming over here to the picture remember that the launching moment is called time equals to zero so clearly it must hit the ground at a time greater than zero and if you're kind of curious like i was showing you on the homework there is a reason why there is a negative time and the equations treat it as a constant acceleration so it treats it for all negative times and all positive times and obviously you could not calculate where it's going to be after a hundred seconds that wouldn't work because it hits the floor but the formula would tell you it's way down here somewhere after 100 seconds but the formula would also tell you that for a small amount of negative time it's on its way up to get to hear it zero which it didn't really happen so that's why we ignore that one just like anything after it hits the ground we wouldn't say that's where it is we ignore those numbers in fact this one i can probably give you i got a negative .175 for that time and seconds it's this one here that is the positive one so again without giving that number away and making you kind of go through the calculation i'm hoping you got a number that was greater than one second but less than two seconds it kind of makes sense fire one one thousand two and it's gonna hit before two seconds but more than one second in fact it's even before a second and a half so between one second and a second and a half is when it hits now the main part of this problem though was to once you solve this harder one for time you could put it back into the x motion and figure out how far it will go and i got a number here too and again without telling it to you let me say that it is more than four meters it is even more than four and a half meters but it is not five meters and so the last step i will do here together is to put a target at where i calculated it and see if i can hit the target all right so i have put if you want to bring the camera over here ron here is the four meters and here is more than 4 meters and so i think it's going to hit right about here actually i calculated right about here but i put it at the back because i do know from experience that when i angle the cannon up it does fire a little slower than when i was firing it horizontally and we did all of our calculations with the idea that it would fire at the same speed and it and it does not so to give myself a little bit of extra leeway i put the calculation distance at the back of the target and hopefully then it'll land somewhere just shy because of the smaller speed because i have it angled up all right well let's give it a try although the other thing i want to test click click click and then i'll check the angle here so we're still at 59 is i know that as i'm messing with it it can kind of turn a little bit so i'm just going to kind of look up the spine and make sure that my cannonball doesn't land just to the left or the right it'd be terrible if i got the right distance and then i'm off to the left it's like ah i did it and i missed so i think i got it right i think i looked up the spine really well and let's give it a try and see if i hit the target so on the count of three i'll fire one two three oh yeah and we got the target and as you can see it was just a little bit shy of what we calculated because of the lower speed so what are you going to turn in these calculations so do your calculations that would include the first big step what is the initial speed that your cannon fires or our cannon fires and then finally how far would it go when you set it up at this angle of 59 degrees and then if you look there the last part of the instruction said put a target there and shoot at it and that's where i came into the picture i'm your hands so i put the target there and we and we hit it so hopefully you're looking at four points and i'll leave it to you alright until next time take care