00:02
In this problem, we have a rocket which initially has the engine moving and then the engine cuts off.
00:08
So i'm going to take my givens and separate it to with the engine and without the engine.
00:15
And so it blasts off and when they blast off, they start from an initial speed of zero.
00:20
And this rocket has an acceleration as 13 meters per second squared and it reaches a height, i put y because it's my vertical displacement, of 25 meters when that engine shuts off.
00:33
And so first let's find the speed it is moving.
00:37
I'll put, let me fix that here.
00:39
I'm gonna put vf for v final just so we know which one we're talking about.
00:43
So let's find the final speed it's moving because we're going to need that in a second when that engine shuts off.
00:49
And so we're going to use the equation final velocity squared is equal to initial velocity squared plus two times acceleration times our displacement.
00:58
That initial velocity is zero so we can take that out.
01:01
To get rid of that square you're going to take the square root of both sides.
01:04
We have two times acceleration times displacement all under our square root.
01:09
And so we have two times 13 times 25 and then you take the square root of that and you get a final velocity in the vertical when that engine shuts off of 25 .5.
01:24
And i wrote a 2.
01:27
25 .5 meters per second.
01:29
And so now we know how fast it's moving when that engine shuts off.
01:32
The reason we need to know that is because the final velocity when it shuts off is the initial velocity without the engine.
01:40
It's the same instant.
01:41
We know it's going to reach a maximum height when it runs out of speed.
01:47
So our final velocity in the upward motion is zero.
01:51
And then the acceleration without the engine is simply going to be that of gravity.
01:56
So the first thing we're asked to find is the maximum height attained by the rocket.
02:01
And so we know the height it attains with the engine.
02:04
Let's find its height without the engine using that same equation we used to start with.
02:09
Okay so our first question we're going to use final velocity squared is equal to initial velocity squared plus two times acceleration times our vertical displacement.
02:20
So we're going to subtract initial velocity on both sides and then divide by two and acceleration.
02:32
And so our equation for the height reached without the engine is going to be final velocity squared minus initial velocity squared divided by two times acceleration.
02:42
So our final velocity for the second part we've already found to be zero minus 25 .5 squared.
02:51
That is squared before that negative is in there.
02:54
Divided by two times negative 9 .8.
02:58
And so our vertical height reached without the engine is going to be negative 25 from the first part plus the 33 .2.
03:15
And from that you get 58 .2 meters is the total height reached by this rocket.
03:24
So that's the first question.
03:25
The second question is what is the speed of the rocket just before it hits the ground.
03:30
And so that is a different part completely.
03:32
That is on the way down.
03:35
And so we have an initial velocity of zero in this case because it's reached maximum height.
03:39
It stops and then it falls back to the ground.
03:42
We know acceleration is that due to gravity because it's in free fall...