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How to solve 2-D projectile motion

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A SmartBoard video (Khan-Academy style) how to solve 2-D problems like where to put the pillow if you roll a golden egg off of the giant's table.

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you're the soccer ball you kick it at 13 years of second my apologies are price your pic 20 meters a second 30 meters of semi 40 there's nothing wrong with turn problem is the house of this 30 degree angle because so many from a with 30-60-90 triangles but I probably shouldn't have my initial velocity and the angle the same but suck it up and do what we can the whole point of chapter 3 is say I want you to chapter two but I'd like you put it in two dimensions my coordinate system  I've got this guy flying at 30 meters a second but I don't want you to think of it is 30 I want you to think of it is he's moving sideways vested extra action and he's moving upward to the Y directions to start with  so I don't want you skip the 30 I want you to think of it as he is moving at 30  sine of 30 to begin with do you know what let me do insert page thing here  okay there's our initial condition let's go to say we have a soccer ball which is being kicked if you take it straight up going to come straight back down doesn't do me any good if you kick it on the ground it's a 2-0 of than the other sides are you going to get it okay we're doing a goal hear you on the 6-yard the guy backed up about 8 yards run move to down goes a certain distance down the field of course the harder you kick it the further down the feel is going to go whatever like you to do is be able to figure out how long is it going to be in the air 5 Seconds and it goes up and comes all the way back down to the ground if it started on the ground and it and it on the ground how far am I on any up down  0p I haven't really gone anywhere yet no look I realize I really have done some I did go certain distance update but then I came back down - 50 if you will and I went 50-50 is zero I haven't really gone anywhere so I can look at this as Midas placement which means net distance with Direction in the y direction is zero  and while I'm in the air I'm going to accelerate in the downward Direction nine point 89.1 I just rounded off 29.8 today velocity I'm telling you is 30 but let's go back to other painter and see if what kind of look at that here  yesterday we discussed that the sine of the angle  is by definition the length of the office that leg over the hypotenuse leg we've been our particular case here is  my starting lacity in the y direction and I am told  that is initial velocity VI is equal to 30 so let's go by subway over 30  is equal to  the sine of 30 degrees  because initial if I plug in my calculator I'll find the sine of 30 is equal to .50 is equal to VI Subway  over 30 so that begs the question What number divided by 30 is .5 in the course you just ripped out for 1515 / 30 is 1/2 what lets me little more math play rigorous on the X 30 I'll have the Subway is equal to 15 that means we're at 30 meters a second at a 30 degree angle from the horizontal what I'm really doing it I'm kicking Upward at 15 plus  so this guy over here is 15 can I get a finger count please on how I came up with the initial velocity upward is 15 recording the fearnow Trebek live the horizontal component is looks like 2526 maybe about 27 ish the vertical component hoops  Roku component that we found to be about 15 and we said that from the origin to are green. Over here we said was 30 how to request a walk through this again the sine of the angle is 30 probably or 5:30 is my definition the opposite leg divided by the hypotenuse you told was 31 how long the opposite leg is so you have the opposite leg than dishwashing the y direction divided by 30 is equal to the sine of the angle so I got 30 times the sine of the angle should equal to Visa by she's multiply both sides by 30 and it works out to 15 and we physically measured it out  5.5 this is .5 so let me look at this other area over here I'll move the recorder thing up to here let's try to figure out with a green arrow is  the cosine of the 30° should equal to my starting block velocity the extra action over whatever my hypotenuse was which is 30 full size my 30 I'll find out what my starting to wasi was in the extraction so my starting the last in the x-direction will be however hard the bar was going to start with I should say fastball was going to start with 30 times the cosine house and Escape 30° find out what it is  works out to be  25 .98  which is what I think we had over here what's in our limits of our reading here on our scale  shut off right here it's pretty darn close to 26th which is what we expected question okay question is mr. Duncan could we have found it via tangent could we have said that the Tangent 30 degrees is equal 15 / the green one you could have said a squared plus b squared is equal to c squared wish you were told the sturdy that was the hypotenuse already found this guy to be 15 225  plus b squared is equal to 900 what's obesity equal to 900 - 225 all square rooted and if you punch out your calculator and bet you going to come out to here's one is a soccer ball and I want to know how long it take to reach stop and people want to do this  look up the 30-degree thing going on well that's for 30 degrees he went to 30 degrees look it's going to end up here but grabbing to Port down something and people are wanted to use Pythagorean theorem and stuff like this when it's not the not triangle 180 degrees okay so what's come on back  until we have to see here my starting velocity is 30 m second time to sine of 30° in the vertical Direction my velocity when I hit the ground it turns out we'll be the same speed as I was going up but downward I would like to figure out how far down the field the ball that you can hit the ground this is you playing AYSO soccer with a little kids the other crazy get get me on hit in the head so they let hit the ground a minute plant my key to finding this is how long it's up in the air because I know that the sideways velocity we just found it out to be is a 25.98 what is the ball was in the air for one second it's going to go 25.98 meters down I need to figure out how long it's actually in the air so here's what I'm going to do in my upper right hand morning  for my why Dimensions only and by the way I will be giving the same lecture again tomorrow  and probably on Monday Kelly till we get it down okay I just have like a preview thing and then we're going to do it again we going to do it again we're going to get it down  my change elevation of my change and why it start on the ground in the ground zero  my acceleration is -9.8 by the way what's making that 9.8  gravity Xbox and how much does gravity pull you sideways it doesn't that's why they celeration is zero in the extraction anyway coming back to our equations up here in the upper right hand it should be half of -9.8  D squared + 50 8 is equal to 0 bring the minus 4.9 t-square to the left hand side becomes positive I can cancel out at T stall 40 it's in the air for 3.06 seconds now that I know the balls in the air for 3.06 seconds all they have to do is figure out how fast it's moving sideways which Rarity did 25.98 quiet by 3.06 which we did here in red and if I did my math correctly it's 79.53 meters down seal that's quite a kick that's going goal kick almost over to the other guy's pendley area  30 m the second is ice I figured out one time in miles per hour is 65 something like that miles an hour that's  the squad if you're going 65 miles an hour down the freeway you put your face out the window I don't recommend it was getting to be a Labrador Retriever or something like that what's the different story put your favorite to win a lot of air resistance you take a soccer ball which is close to the size of that kid's head it's like 65 miles an hour soon as it leaves his foot down quite a bit 25.98 m per second sideways to start with but after it's gone ashore distance it slowed down quite a bit you know this you play soccer and the other guys have a direct free-kick and uniforming the walls and he gets five guys up there and they are kind of staying like this the guy texted you kick straight ask you if your legs that kind of stunt but it's gone halfway down the field it doesn't hurt so much slow down quite a bit  so in theory with no air resistance it would go 79.5 3M downfield but reality is going to be significantly less than that what is the steps to get  put your X and Y component start out with why because you need to find out how long it's in the air  you want to start with why because you know what assets you know it's going to end up back on the ground that's one additional piece of information that you have  sat vif get free write down your known to your unknown  at 4 Destin equation which we did the upper right-hand side here is 1/2 a t square plus vit for only looking at the Y Dimensions step 5 plug-in trucks all these for the time  denounce you have the time you can plug it in for the X Dimensions which I didn't read to change there you go? 79.50 did you actually do 30 cosine 30 * 3.06 42 - 25. play  SI unit for the slightly different answer in mind it's just question how many numbers we kept in the South later Lapeer time  is 3.06 be a time when I actually work this out for the time I kept the numbers in my calculator we had * 3.0 Nexus not actually 3.06 by 3.06 did the did that little extra did the is enough to give you just slightly more if I were grading this what I would do is answer the answer is 79.5 customize a little bit on that 5 porcelain 57.6 good enough set alarm at live around doctor sometimes I have two tents how to question question get tomorrow I want us to be able to do this from is similar  I think it's actually easier this one you're on top of the table and you something off you want to know where to put the trash can door to caption  where is what are one  you come out on flat ground but you end up having an angle  this one here you start out flat  but you end up down at a lower elevation ultimately where we like to do is kind of put both of those together where you have a change in elevation and  you start out not going flat the first one we start out with flat ground but you had an angle the second one you have no angle but you don't have flat ground the third one you doing both okay so you got to come by this this this one's a little bit more tricky  and I will work that out I've got a question for you  Andrew how long you live in California  16 years your whole life great great  I assume you know the ABCs  please in 5 seconds or less say the ABC ABCD EFG HIJK LMNOP QRS TUV WX y&z very close set them incorrectly try again  A B C D E F G H I J K L M N O P I'm sorry can you take it please from h i j k l m n o p q r s t u v w Treasure of the difference do it quickly starting from me t h i g h i j k l m n o p what the heck is Elemental Elemental in a mineral is it something else small little fish little mental Elemental I assume you've learned it by singing it  good HHH ABCD g h i j k l m n o p  look Honey Singh before he he doesn't know the words to he's messing up twinkle twinkle little star how I wonder where you are or what you are up above the world so high like a diamond in the sky there are too many syllables  LMNO P.... It's a song you learn to be a music if you went to the United States but was really fun is to talk to somebody say from Sri Lanka only been here for 6 months they didn't learn it via Twinkle Twinkle Little Star so they don't do LMNO five interesting there is no substitute repetition  I know how to shoot a basket horrible but I know how to do it elbow pointer at The Basque do you want to form a plane between your shoulder your elbow your wrist you take your wrist you twist all the way as far as you can to the right Sumi right-handed and you bro does Maya make it but the reason they have to shoot and shoot and shoot your since your muscles memory so then you get up there if you're good you mean look  not you know what you're doing I mean what the baskets moved  you got there you look make sure you feed the right place close your eyes and inferior you should will do 30 of these in a row in theory now car like that little while I'm a wax on wax off still Shogun things then thing going on your kind of shoot it shoot the arrow and then shoot the arrow exploited is there a you should all do it is Siri what you need to do on these guys some again and again and again do it again becomes boring do it twice more to where you don't have to think about it it just flows if you do that you're good night  if you have to sit in look at it  hopefully good night  accident

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How to solve 2-D projectile motion

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