[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.67,0:00:05.44,Default,,0000,0000,0000,,This right here is a picture\Nof an Airbus A380 aircraft.
Dialogue: 0,0:00:05.44,0:00:08.11,Default,,0000,0000,0000,,And I was curious\Nhow long would it
Dialogue: 0,0:00:08.11,0:00:10.79,Default,,0000,0000,0000,,take this aircraft to take off?
Dialogue: 0,0:00:10.79,0:00:12.88,Default,,0000,0000,0000,,And I looked up its\Ntakeoff velocity.
Dialogue: 0,0:00:17.57,0:00:23.60,Default,,0000,0000,0000,,And the specs I got were\N280 kilometers per hour.
Dialogue: 0,0:00:23.60,0:00:26.81,Default,,0000,0000,0000,,And to make this a velocity we\Nhave to specify a direction as
Dialogue: 0,0:00:26.81,0:00:28.62,Default,,0000,0000,0000,,well, not just a magnitude.
Dialogue: 0,0:00:28.62,0:00:31.68,Default,,0000,0000,0000,,So the direction is in the\Ndirection of the runway.
Dialogue: 0,0:00:31.68,0:00:35.30,Default,,0000,0000,0000,,So that would be the positive\Ndirection right over there.
Dialogue: 0,0:00:35.30,0:00:37.47,Default,,0000,0000,0000,,So when we're talking about\Nacceleration or velocity
Dialogue: 0,0:00:37.47,0:00:38.93,Default,,0000,0000,0000,,in this, we're\Ngoing to assume it's
Dialogue: 0,0:00:38.93,0:00:42.78,Default,,0000,0000,0000,,in this direction, the direction\Nof going down the runway.
Dialogue: 0,0:00:42.78,0:00:44.97,Default,,0000,0000,0000,,And I also looked up\Nits specs, and this,
Dialogue: 0,0:00:44.97,0:00:47.12,Default,,0000,0000,0000,,I'm simplifying a little\Nbit, because it's not
Dialogue: 0,0:00:47.12,0:00:49.21,Default,,0000,0000,0000,,going to have a purely\Nconstant acceleration.
Dialogue: 0,0:00:49.21,0:00:50.63,Default,,0000,0000,0000,,But let's just say\Nfrom the moment
Dialogue: 0,0:00:50.63,0:00:53.49,Default,,0000,0000,0000,,that the pilot says we're\Ntaking off to when it actually
Dialogue: 0,0:00:53.49,0:00:55.69,Default,,0000,0000,0000,,takes off it has a\Nconstant acceleration.
Dialogue: 0,0:00:55.69,0:01:02.28,Default,,0000,0000,0000,,Its engines are able to\Nprovide a constant acceleration
Dialogue: 0,0:01:02.28,0:01:09.96,Default,,0000,0000,0000,,of 1.0 meters per\Nsecond per second.
Dialogue: 0,0:01:09.96,0:01:13.07,Default,,0000,0000,0000,,So after every second it\Ncan go one meter per second
Dialogue: 0,0:01:13.07,0:01:16.03,Default,,0000,0000,0000,,faster than it was going at\Nthe beginning of that second.
Dialogue: 0,0:01:16.03,0:01:25.53,Default,,0000,0000,0000,,Or another way to write this\Nis 1.0-- let me write it
Dialogue: 0,0:01:25.53,0:01:27.25,Default,,0000,0000,0000,,this way-- meters\Nper second per second
Dialogue: 0,0:01:27.25,0:01:30.98,Default,,0000,0000,0000,,can also be written as\Nmeters per second squared.
Dialogue: 0,0:01:30.98,0:01:32.65,Default,,0000,0000,0000,,I find this a little\Nbit more intuitive.
Dialogue: 0,0:01:32.65,0:01:34.91,Default,,0000,0000,0000,,This is a little\Nbit neater to write.
Dialogue: 0,0:01:34.91,0:01:36.36,Default,,0000,0000,0000,,So let's figure this out.
Dialogue: 0,0:01:36.36,0:01:38.49,Default,,0000,0000,0000,,So the first thing\Nwe're trying to answer
Dialogue: 0,0:01:38.49,0:01:42.54,Default,,0000,0000,0000,,is, how long does take off last?
Dialogue: 0,0:01:47.36,0:01:50.20,Default,,0000,0000,0000,,That is the question\Nwe will try to answer.
Dialogue: 0,0:01:50.20,0:01:52.40,Default,,0000,0000,0000,,And to answer this,\Nat least my brain
Dialogue: 0,0:01:52.40,0:01:54.29,Default,,0000,0000,0000,,wants to at least\Nget the units right.
Dialogue: 0,0:01:54.29,0:01:55.83,Default,,0000,0000,0000,,So over here we have\Nour acceleration
Dialogue: 0,0:01:55.83,0:01:58.89,Default,,0000,0000,0000,,in terms of meters and\Nseconds, or seconds squared.
Dialogue: 0,0:01:58.89,0:02:00.64,Default,,0000,0000,0000,,And over here we have\Nour takeoff velocity
Dialogue: 0,0:02:00.64,0:02:04.13,Default,,0000,0000,0000,,in terms of\Nkilometers and hours.
Dialogue: 0,0:02:04.13,0:02:06.03,Default,,0000,0000,0000,,So let's just convert\Nthis takeoff velocity
Dialogue: 0,0:02:06.03,0:02:07.17,Default,,0000,0000,0000,,into meters per second.
Dialogue: 0,0:02:07.17,0:02:10.48,Default,,0000,0000,0000,,And then it might simplify\Nanswering this question.
Dialogue: 0,0:02:10.48,0:02:14.77,Default,,0000,0000,0000,,So if we have 280\Nkilometers per hour,
Dialogue: 0,0:02:14.77,0:02:18.17,Default,,0000,0000,0000,,how do we convert that\Nto meters per second?
Dialogue: 0,0:02:18.17,0:02:21.63,Default,,0000,0000,0000,,So let's convert it to\Nkilometers per second first.
Dialogue: 0,0:02:21.63,0:02:23.65,Default,,0000,0000,0000,,So we want to get\Nrid of this hours.
Dialogue: 0,0:02:23.65,0:02:25.12,Default,,0000,0000,0000,,And the best way\Nto do that, if we
Dialogue: 0,0:02:25.12,0:02:26.58,Default,,0000,0000,0000,,have an hour in\Nthe denominator, we
Dialogue: 0,0:02:26.58,0:02:29.23,Default,,0000,0000,0000,,want an hour in the\Nnumerator, and we
Dialogue: 0,0:02:29.23,0:02:31.53,Default,,0000,0000,0000,,want a second in\Nthe denominator.
Dialogue: 0,0:02:31.53,0:02:34.60,Default,,0000,0000,0000,,And so what do we\Nmultiply this by?
Dialogue: 0,0:02:34.60,0:02:36.96,Default,,0000,0000,0000,,Or what do we put in front\Nof the hours and seconds?
Dialogue: 0,0:02:36.96,0:02:41.03,Default,,0000,0000,0000,,So one hour, in one hour\Nthere are 3,600 seconds,
Dialogue: 0,0:02:41.03,0:02:44.96,Default,,0000,0000,0000,,60 seconds in a minute,\N60 minutes in an hour.
Dialogue: 0,0:02:44.96,0:02:46.87,Default,,0000,0000,0000,,And so you have one\Nof the larger unit
Dialogue: 0,0:02:46.87,0:02:50.40,Default,,0000,0000,0000,,is equal to 3,600\Nof the smaller unit.
Dialogue: 0,0:02:50.40,0:02:52.28,Default,,0000,0000,0000,,And that we can\Nmultiply by that.
Dialogue: 0,0:02:52.28,0:02:54.82,Default,,0000,0000,0000,,And if we do that, the\Nhours will cancel out.
Dialogue: 0,0:02:54.82,0:02:58.95,Default,,0000,0000,0000,,And we'll get 280 divided by\N3,600 kilometers per second.
Dialogue: 0,0:02:58.95,0:03:00.83,Default,,0000,0000,0000,,But I want to do\Nall my math at once.
Dialogue: 0,0:03:00.83,0:03:04.55,Default,,0000,0000,0000,,So let's also do the conversion\Nfrom kilometers to meters.
Dialogue: 0,0:03:04.55,0:03:08.77,Default,,0000,0000,0000,,So once again, we have\Nkilometers in the numerator.
Dialogue: 0,0:03:08.77,0:03:11.07,Default,,0000,0000,0000,,So we want the kilometers\Nin the denominator now.
Dialogue: 0,0:03:11.07,0:03:12.41,Default,,0000,0000,0000,,So it cancels out.
Dialogue: 0,0:03:12.41,0:03:14.49,Default,,0000,0000,0000,,And we want meters\Nin the numerator.
Dialogue: 0,0:03:14.49,0:03:15.71,Default,,0000,0000,0000,,And what's the smaller unit?
Dialogue: 0,0:03:15.71,0:03:16.79,Default,,0000,0000,0000,,It's meters.
Dialogue: 0,0:03:16.79,0:03:20.80,Default,,0000,0000,0000,,And we have 1,000 meters\Nfor every 1 kilometer.
Dialogue: 0,0:03:20.80,0:03:22.83,Default,,0000,0000,0000,,And so when you multiply\Nthis out the kilometers
Dialogue: 0,0:03:22.83,0:03:23.91,Default,,0000,0000,0000,,are going to cancel out.
Dialogue: 0,0:03:23.91,0:03:29.49,Default,,0000,0000,0000,,And you are going to be\Nleft with 280 times 1,
Dialogue: 0,0:03:29.49,0:03:35.62,Default,,0000,0000,0000,,so we don't have to write\Nit down, times 1,000,
Dialogue: 0,0:03:35.62,0:03:43.40,Default,,0000,0000,0000,,all of that over 3,600,\Nand the units we have left
Dialogue: 0,0:03:43.40,0:03:49.44,Default,,0000,0000,0000,,are meters per-- and the\Nonly unit we have left here
Dialogue: 0,0:03:49.44,0:03:52.70,Default,,0000,0000,0000,,is second-- meters per second.
Dialogue: 0,0:03:52.70,0:03:57.97,Default,,0000,0000,0000,,So let's get my trusty TI-85\Nout and actually calculate this.
Dialogue: 0,0:03:57.97,0:04:03.05,Default,,0000,0000,0000,,So we have 280 times 1000, which\Nis obviously 280,000, but let
Dialogue: 0,0:04:03.05,0:04:06.79,Default,,0000,0000,0000,,me just divide that by 3,600.
Dialogue: 0,0:04:06.79,0:04:10.88,Default,,0000,0000,0000,,And it gives me 77.7\Nrepeating indefinitely.
Dialogue: 0,0:04:10.88,0:04:13.30,Default,,0000,0000,0000,,And it looks like I had\Ntwo significant digits
Dialogue: 0,0:04:13.30,0:04:15.12,Default,,0000,0000,0000,,in each of these\Noriginal things.
Dialogue: 0,0:04:15.12,0:04:18.23,Default,,0000,0000,0000,,I had 1.0 over\Nhere, not 100% clear
Dialogue: 0,0:04:18.23,0:04:20.63,Default,,0000,0000,0000,,how many significant\Ndigits over here.
Dialogue: 0,0:04:20.63,0:04:23.83,Default,,0000,0000,0000,,Was the spec rounded to\Nthe nearest 10 kilometers?
Dialogue: 0,0:04:23.83,0:04:26.80,Default,,0000,0000,0000,,Or is it exactly 280\Nkilometers per hour?
Dialogue: 0,0:04:26.80,0:04:28.34,Default,,0000,0000,0000,,Just to be safe I'll\Nassume that it's
Dialogue: 0,0:04:28.34,0:04:30.36,Default,,0000,0000,0000,,rounded to the\Nnearest 10 kilometers.
Dialogue: 0,0:04:30.36,0:04:32.39,Default,,0000,0000,0000,,So we only have two\Nsignificant digits here.
Dialogue: 0,0:04:32.39,0:04:34.26,Default,,0000,0000,0000,,So we should only have\Ntwo significant digits
Dialogue: 0,0:04:34.26,0:04:34.91,Default,,0000,0000,0000,,in our answer.
Dialogue: 0,0:04:34.91,0:04:41.39,Default,,0000,0000,0000,,So we're going to round this\Nto 78 meters per second.
Dialogue: 0,0:04:41.39,0:04:48.80,Default,,0000,0000,0000,,So this is going to be\N78 meters per second,
Dialogue: 0,0:04:48.80,0:04:50.95,Default,,0000,0000,0000,,which is pretty fast.
Dialogue: 0,0:04:50.95,0:04:53.59,Default,,0000,0000,0000,,For this thing to take off\Nevery second that goes by it
Dialogue: 0,0:04:53.59,0:04:58.26,Default,,0000,0000,0000,,has to travel 78\Nmeters, roughly 3/4
Dialogue: 0,0:04:58.26,0:05:01.37,Default,,0000,0000,0000,,of the length of a football\Nfield in every second.
Dialogue: 0,0:05:01.37,0:05:03.16,Default,,0000,0000,0000,,But that's not what\Nwe're trying to answer.
Dialogue: 0,0:05:03.16,0:05:05.95,Default,,0000,0000,0000,,We're trying to say how\Nlong will take off last?
Dialogue: 0,0:05:05.95,0:05:09.65,Default,,0000,0000,0000,,Well we could just do this in\Nour head if you think about it.
Dialogue: 0,0:05:09.65,0:05:12.44,Default,,0000,0000,0000,,The acceleration is 1 meter\Nper second, per second.
Dialogue: 0,0:05:12.44,0:05:15.06,Default,,0000,0000,0000,,Which tells us\Nafter every second
Dialogue: 0,0:05:15.06,0:05:17.42,Default,,0000,0000,0000,,it's going 1 meter\Nper second faster.
Dialogue: 0,0:05:17.42,0:05:21.57,Default,,0000,0000,0000,,So if you start at a velocity\Nof 0 and then after 1 second
Dialogue: 0,0:05:21.57,0:05:22.99,Default,,0000,0000,0000,,it'll be going 1\Nmeter per second.
Dialogue: 0,0:05:22.99,0:05:25.20,Default,,0000,0000,0000,,After 2 seconds it will be\Ngoing 2 meters per second.
Dialogue: 0,0:05:25.20,0:05:27.74,Default,,0000,0000,0000,,After 3 seconds it'll be\Ngoing 3 meters per second.
Dialogue: 0,0:05:27.74,0:05:30.77,Default,,0000,0000,0000,,So how long will it take to\Nget to 78 meters per second?
Dialogue: 0,0:05:30.77,0:05:38.55,Default,,0000,0000,0000,,Well, it will take 78\Nseconds, or roughly a minute
Dialogue: 0,0:05:38.55,0:05:40.71,Default,,0000,0000,0000,,and 18 seconds.
Dialogue: 0,0:05:40.71,0:05:44.84,Default,,0000,0000,0000,,And just to verify this with our\Ndefinition of our acceleration,
Dialogue: 0,0:05:44.84,0:05:46.88,Default,,0000,0000,0000,,so to speak, just\Nremember acceleration,
Dialogue: 0,0:05:46.88,0:05:48.96,Default,,0000,0000,0000,,which is a vector quantity,\Nand all the directions
Dialogue: 0,0:05:48.96,0:05:51.06,Default,,0000,0000,0000,,we're talking about now\Nare in the direction
Dialogue: 0,0:05:51.06,0:05:53.28,Default,,0000,0000,0000,,of this direction of the runway.
Dialogue: 0,0:05:53.28,0:06:00.24,Default,,0000,0000,0000,,The acceleration is equal\Nto change in velocity
Dialogue: 0,0:06:00.24,0:06:02.14,Default,,0000,0000,0000,,over change in time.
Dialogue: 0,0:06:04.68,0:06:07.05,Default,,0000,0000,0000,,And we're trying to solve for\Nhow much time does it take,
Dialogue: 0,0:06:07.05,0:06:08.74,Default,,0000,0000,0000,,or the change in time.
Dialogue: 0,0:06:08.74,0:06:09.52,Default,,0000,0000,0000,,So let's do that.
Dialogue: 0,0:06:09.52,0:06:12.04,Default,,0000,0000,0000,,So let's multiply both\Nsides by change in time.
Dialogue: 0,0:06:12.04,0:06:17.78,Default,,0000,0000,0000,,You get change in time\Ntimes acceleration
Dialogue: 0,0:06:17.78,0:06:20.78,Default,,0000,0000,0000,,is equal to change in velocity.
Dialogue: 0,0:06:24.18,0:06:26.60,Default,,0000,0000,0000,,And to solve for change\Nin time, divide both sides
Dialogue: 0,0:06:26.60,0:06:29.23,Default,,0000,0000,0000,,by the acceleration.
Dialogue: 0,0:06:29.23,0:06:31.94,Default,,0000,0000,0000,,So divide both sides by\Nthe acceleration you get
Dialogue: 0,0:06:31.94,0:06:33.98,Default,,0000,0000,0000,,a change in time.
Dialogue: 0,0:06:33.98,0:06:35.71,Default,,0000,0000,0000,,I could go down\Nhere, but I just want
Dialogue: 0,0:06:35.71,0:06:37.58,Default,,0000,0000,0000,,to use all this real\Nestate I have over here.
Dialogue: 0,0:06:37.58,0:06:40.40,Default,,0000,0000,0000,,I have change in time\Nis equal to change
Dialogue: 0,0:06:40.40,0:06:44.86,Default,,0000,0000,0000,,in velocity divided\Nby acceleration.
Dialogue: 0,0:06:47.92,0:06:51.66,Default,,0000,0000,0000,,And in this situation, what\Nis our change in velocity?
Dialogue: 0,0:06:51.66,0:06:53.46,Default,,0000,0000,0000,,Well, we're starting\Noff with the velocity,
Dialogue: 0,0:06:53.46,0:06:54.98,Default,,0000,0000,0000,,or we're assuming\Nwe're starting off
Dialogue: 0,0:06:54.98,0:06:57.88,Default,,0000,0000,0000,,with a velocity of\N0 meters per second.
Dialogue: 0,0:06:57.88,0:07:00.71,Default,,0000,0000,0000,,And we're getting up to\N78 meters per second.
Dialogue: 0,0:07:00.71,0:07:04.65,Default,,0000,0000,0000,,So our change in velocity\Nis the 78 meters per second.
Dialogue: 0,0:07:09.23,0:07:11.03,Default,,0000,0000,0000,,So this is equal,\Nin our situation,
Dialogue: 0,0:07:11.03,0:07:14.58,Default,,0000,0000,0000,,78 meters per second is\Nour change in velocity.
Dialogue: 0,0:07:14.58,0:07:17.40,Default,,0000,0000,0000,,I'm taking the final velocity,\N78 meters per second,
Dialogue: 0,0:07:17.40,0:07:19.32,Default,,0000,0000,0000,,and subtract from that\Nthe initial velocity,
Dialogue: 0,0:07:19.32,0:07:20.59,Default,,0000,0000,0000,,which is 0 meters per second.
Dialogue: 0,0:07:20.59,0:07:22.00,Default,,0000,0000,0000,,And you just get this.
Dialogue: 0,0:07:22.00,0:07:24.23,Default,,0000,0000,0000,,Divided by the\Nacceleration, divided
Dialogue: 0,0:07:24.23,0:07:28.99,Default,,0000,0000,0000,,by 1 meter per\Nsecond per second,
Dialogue: 0,0:07:28.99,0:07:31.40,Default,,0000,0000,0000,,or 1 meter per second squared.
Dialogue: 0,0:07:31.40,0:07:33.16,Default,,0000,0000,0000,,So the numbers part\Nare pretty easy.
Dialogue: 0,0:07:33.16,0:07:36.92,Default,,0000,0000,0000,,You have 78 divided by\N1, which is just 78.
Dialogue: 0,0:07:36.92,0:07:40.14,Default,,0000,0000,0000,,And then the units you\Nhave meters per second.
Dialogue: 0,0:07:40.14,0:07:42.62,Default,,0000,0000,0000,,And then if you divide by\Nmeters per second squared,
Dialogue: 0,0:07:42.62,0:07:44.23,Default,,0000,0000,0000,,that's the same\Nthing as multiplying
Dialogue: 0,0:07:44.23,0:07:46.76,Default,,0000,0000,0000,,by seconds squared per meter.
Dialogue: 0,0:07:46.76,0:07:48.44,Default,,0000,0000,0000,,Right?
Dialogue: 0,0:07:48.44,0:07:49.94,Default,,0000,0000,0000,,Dividing by something\Nthe same thing
Dialogue: 0,0:07:49.94,0:07:51.94,Default,,0000,0000,0000,,as multiplying by\Nits reciprocal.
Dialogue: 0,0:07:51.94,0:07:54.13,Default,,0000,0000,0000,,And you can do the\Nsame thing with units.
Dialogue: 0,0:07:54.13,0:07:57.11,Default,,0000,0000,0000,,And then we see the\Nmeters cancel out.
Dialogue: 0,0:07:57.11,0:07:59.06,Default,,0000,0000,0000,,And then seconds squared\Ndivided by seconds,
Dialogue: 0,0:07:59.06,0:08:00.66,Default,,0000,0000,0000,,you're just left with seconds.
Dialogue: 0,0:08:00.66,0:08:04.34,Default,,0000,0000,0000,,So once again, we\Nget 78 seconds,
Dialogue: 0,0:08:04.34,0:08:07.91,Default,,0000,0000,0000,,a little over a minute for\Nthis thing to take off.