00:01
Okay, an object falls from h.
00:05
So it's going to start at h, and v initial is zero, because it's starting from rest.
00:13
It travels 0 .50h in the last one second.
00:27
Okay.
00:30
Time and height that it falls.
00:33
Okay.
00:34
So, v squared equals v initial squared minus 2g delta y.
01:01
The delta y here is going to be h minus 0 .5h for the beginning of the fall.
01:11
So, v, by the way, v0 is 0, is going to equal the square.
01:18
Root of 2g times h minus 0 .5h, which is just going to be 0 .5h.
01:38
I'm going to call that one -half h.
01:41
Okay, simplifying, v is going to be the square root of gh.
01:49
And this will be v sub.
01:52
I'm going to call this v.
01:54
2, because it's at halfway down.
02:00
Okay, but we want the time and height of the total fall.
02:12
The total fall, let me think about this again.
02:23
It travels that far in the last half a second.
02:30
Okay, so in the last half of a second, because this was the first half of a second, now let's do the last half of a second.
02:37
Now let's do the second.
02:40
V final, which would be like the, i'm going to call that three squared, equals, but wait, i know time here, and i know height.
02:59
So i'm going to use both, v initial squared.
03:12
Now, everything's in the downward direction, but we square it.
03:24
So then the velocities, but i know that v3 is going to be larger.
03:32
Than v2.
03:33
So i need to add 2g and then again it's going to be one half of h.
03:46
So v3 is going to be the square root of v2 squared plus gh.
03:57
So now i've got v2, v3, and h that are unknowns.
04:11
Okay, let's keep going.
04:19
Y equals y initial.
04:27
Let's try this for the first half.
04:31
Y equals y initial, which would be h plus v initial t.
04:42
Well, v initial would be zero minus one half g t squared, but that would just be t for the first half.
04:58
So i'm going to write, you know what? i'm going to write half of the total time.
05:09
So t is going to be the total time.
05:12
Okay.
05:25
And y is going to be one half h because it's going to fall one half h.
05:41
Okay.
05:43
So from this one, h minus, one half h is one half h.
06:01
Those cancel out.
06:08
Okay? so h over g is going to equal t squared over four.
06:19
And so t is going to equal two square root of h over g.
06:28
So t equals two square root of h over g.
06:39
I didn't put h into my calculator yet.
06:42
Oh, i don't know what h is.
06:44
E, e, e, e, e, okay, so i can't use a calculator yet.
06:51
So now i have three equations, but i don't know t.
06:58
I don't know h.
07:03
I don't know v2 or v3.
07:10
So i think i can do the same thing, but for the bottom half.
07:17
So again, h over 2 is going to equal.
07:24
So y equals y initial.
07:28
Wait a minute.
07:32
For the last half, y final is zero.
07:37
Is going to be y initial minus v2t.
07:49
But this is not going to be the total t.
07:53
This is going to be half of the total t for the second half.
08:06
No, that doesn't make sense.
08:11
Gar.
08:13
Because half the height is not going to be half the time.
08:22
Ooh.
08:23
Half the height not going to be half the time.
08:35
Whoops.
08:37
Okay.
08:38
So half the height is not half the time.
08:41
So that has to go away.
08:43
That has to go away.
08:46
This is the time minus 1, though.
08:53
So i could write the total time is the first time minus 1.
09:03
So i need to write t minus 1 here.
09:09
Okay.
09:11
So now, get all of this out of there.
09:19
Okay, i still have h over g, but now it's going to be t minus 1 squared.
09:31
Okay.
09:32
Because the 1 right up here.
09:35
All right.
09:38
So i take the square root, and that's just going to be t minus 1.
09:44
So this is going to be the square root of h over g minus 1 plus 1.
09:55
Okay.
09:56
Over here then, y equals y initial minus v.
10:04
T, but we know t is 1.
10:06
Here, minus one half g, and again, t is one squared.
10:25
Okay.
10:27
So, this tells me h equals v plus g over two times two.
10:47
Let's take this a little bit slower.
10:48
H over two is going to be v2 plus g over two.
10:54
Then we multiply by 2.
10:56
H is going to be 2 v2 plus g.
11:02
Okay.
11:08
So, hv2, t, and v1 are the unknowns.
11:24
And i've got four equations.
11:27
Four equations and four unknowns, i can solve it.
11:30
Okay.
11:31
Now...