00:01
Once again, welcome to a new problem.
00:05
Think about a rocket that's flying from the surface of the art.
00:09
So let's say this is the art surface.
00:12
And the rocket launches off.
00:17
Obviously, it's going to have an initial velocity when it's launching off.
00:22
There are certain parameters about the rocket.
00:26
Think about this as your initial velocity.
00:30
There are certain parameters.
00:33
Of the rocket that are helpful to solving the problem.
00:37
For example, there is g, which is the acceleration.
00:44
This is the acceleration due to gravity.
00:49
So you're thinking about the acceleration due to gravity.
00:53
There are many other factors that are going to show up in the particular problem.
00:57
One of the other things you're seeing is the fact that the the rocket itself has a mass, you know, before it launches off, the rocket has an initial mass.
01:18
And we want to look at this initial mass as mi, m -sub -script i.
01:24
And then, of course, this time that's going to take place, so the rocket itself is going to launch.
01:33
And now it's going upwards, and there's some time that's fast, so it's going upwards.
01:43
And in that sense, it's going to lose some mass.
01:48
So the initial mass of the rocket and the current mass are not going to be the same.
01:58
So we'll call the current mass m, and so the rocket is going upwards.
02:02
And in this instance we have fuel that's pushing or exhaust, this is the exhaust that's pushing the rocket upwards.
02:18
The initial mass of the rocket is going to burn some fuel, and then the rocket itself has an initial velocity as the fuel as the fuel is burning and going to burn up.
02:34
Upwards.
02:37
The mass and fuel decreases as the rocket goes upwards.
02:49
So these are things that you're seeing.
02:50
The mass and the fuel decreases as the rocket goes upwards.
02:56
The other thing you want to remember is that the sum of the external forces is zero.
03:02
So there's no external we want to say there's no external force acting on the rocket.
03:17
So we don't have external forces acting on the rocket.
03:20
It's just going upwards.
03:23
And as it loses the mass, you know, we'll say as the rocket loses mass, you know, speed so it gains its speed so it's losing its mass and the fuel it's gains its speed these conservation of momentum so that simply means that initial momentum of the rocket is the same as the final momentum of the rocket so we have the initial momentum and the final momentum of the rocket.
04:15
The gravity, as you can see, we do, we still have g, which is the acceleration due to gravity, it's pointed downwards.
04:27
The gravity is pointed downwards, so it affects the speed of the rocket.
04:35
Obviously, it's going to slow it down because gravity is pointing upwards.
04:40
There are such another piece of information that are helpful in solving this problem.
04:45
By the time the rocket goes all the way up, it reaches a speed v of 100 meters per second.
04:56
And this happens at a time t 10 .0 seconds.
05:01
The speed of this exhaust, so the exhausts that you're seeing, those ones too do have their own speed.
05:10
And that speed happens to be 1500.
05:17
So the speed of the exhaust, which we're calling you, is 1 ,500 meters per second.
05:23
That's the speed of the exhaust.
05:26
So the fuel that we've lost, so the fuel that we've lost is 100 kilograms.
05:39
So, meaning if you think about it, the initial mass minus the current mass is going to be 100 kilograms.
05:53
So this is equivalent to the fuel lost in burning.
05:59
So this is equivalent to the fuel lost in burning.
06:03
So the initial mass is equivalent to the difference between the initial mass and the current mass is the same.
06:10
As 100 kilograms.
06:15
So our goal in this problem is to figure out mi, which is what is the initial mass of the rocket.
06:31
That's kind of what we're looking at in this problem.
06:34
We want to find the initial mass of the rocket.
06:37
And so the rocket is taking off the rocket equation.
06:43
If you think about the rocket equation, it's the same as changing velocity.
06:53
This is the change in velocity.
06:59
It's the same as u, l and of initial mass, all of current mass times g delta t.
07:10
G delta t is still equivalent to remember g is meters per second squared, and then delta t is seconds.
07:22
So if you take g delta t, you get meters per second square times second, which is the same as meters per second, which is a velocity.
07:30
It's a form of velocity.
07:32
And this one too is a velocity...