00:01
All right.
00:02
I'm starting to kind of enjoy these problems with drag.
00:07
If you've done as much as me, maybe you would enjoy them too, but i'm not sure.
00:15
Mass, because these are very long.
00:18
The mass is 46 grams.
00:25
I like the numerical modeling, by the way.
00:31
And it strikes the ground 155 meters away.
00:36
So x final is 155 meters.
00:44
Okay.
00:46
Drag force is r equals cv squared.
00:50
R equals cv squared.
00:54
And has a terminal speed.
00:57
Just putting a lot together on this one is 44 meters per second.
01:10
Okay, first i need to calculate c.
01:15
Well, in the book, trying to get to the book here, in the book, it says r, in the example, r equals one -half d, row a, v squared.
01:43
But ours is similar.
01:46
Ours is r equal c v squared.
01:53
So c is 1 half d row a.
01:57
Now, in the book, it says that the terminal velocity draw where are we here, green, the terminal velocity is the square root of 2mg over d r0a.
02:28
Putting this all together, that would be the square root of 2mg over d row a is 2c.
02:36
So it's going to be the square root of mg over c.
02:41
Now, i'm wondering if i had written down mass times acceleration equals mass times gravity minus cv squared.
03:01
And then i solved it, i think i can figure this out, and then i solved it for a, g minus c over mv squared.
03:18
Yeah, when a equals zero, the terminal velocity, just looking at this would be the square root mg over c.
03:33
So i didn't even really need to do this by looking at the book.
03:39
I could have just written this and figured it out.
03:42
Okay.
03:44
But what were we trying to answer here? what is c? so c, well, i'll just continue from here.
04:02
Zero is g minus c over mvt squared.
04:08
Okay, so g equals c over m vt squared.
04:21
So c is going to be gm, c is going to be gm over vt squared.
04:35
Okay, so getting the calculator going, gm over vt squared.
04:45
So g is 9 .81.
04:53
M is 46 grams.
05:03
So i need to write this in kilograms .046.
05:11
Yeah, gm over vt squared, which is 44.
05:24
Okay, so that's gonna be this number for c.
05:33
Okay, now, numerical method, the initial velocity makes an angle of 31 degrees.
05:48
Now, i saved what i did last time, and it's a good thing i did because i think this is going to be very much like it.
05:56
So, y starts out at zero, but it's 31 degrees.
06:15
So theta is going to be 31.
06:18
1.
06:19
M is 0 .046.
06:26
There's no b anymore.
06:28
There's a c.
06:31
And the c is going to be, i'm going to copy that from my calculator here.
06:42
Copy, and i'm going to paste it in here.
06:48
Paste.
06:49
Okay, so i've got mcg, i've got a delta t of 0 .05, which i think i'm going to let go.
06:59
Now, now, now, now, now, now, now, now, now, now, now, now, now, now, no, now, now, no, no, now, now, no, no, no, no, no.
07:08
My equation is not correct because i was using the one from last time.
07:15
So let's work on this.
07:17
A is dv over d t, which can be approximated as delta v over delta t, which is g minus c over m v squared.
07:31
So delta v is going to be g minus c over m v squared times delta t.
07:41
So, here.
07:52
So this is h4.
07:58
H4 is g.
08:02
I think this should be minus.
08:12
C over m v squared times delta t and then we add that to v.
08:28
Okay, good.
08:32
Now in the x direction, we don't have g, but we've got everything else.
08:39
So it would be c over m, v, square.
08:52
So i need to square that.
09:00
Okay.
09:02
Now, my problem is that i don't know the initial velocity.
09:10
So let's say that v equals 100.
09:19
Oops.
09:27
Okay, if v equals 100, then this would be v.
09:38
Whoops, don't know why i did that.
09:40
Maybe you have to delete this and then click over here maybe.
09:47
100 sine theta.
09:52
Okay.
09:55
And this would be 100 cosine theta.
10:09
That's cool.
10:10
The f4 button's working.
10:12
I wonder why it didn't work my other device.
10:16
Okay.
10:18
A hundred.
10:21
And i do want the f4.
10:26
Okay.
10:33
Though i don't really need it because it's only being referenced in those two places.
10:38
Okay.
10:40
So now, i need to drag this down as far as it'll go.
10:57
There's probably a better way to do this, but i don't know what the better way is.
11:05
Uh -oh, something's not right here, but that's getting really, really big.
11:22
And i don't want it to get really, really big.
11:27
So maybe i'm supposed to have a plus in here.
11:42
And now i'll drag it down.
11:54
Still gives me an error.
12:06
Okay.
12:07
So something's wrong.
12:15
V -y and vx.
12:17
So wait a minute.
12:19
Vx.
12:20
Vx.
12:20
Vx.
12:20
Vx.
12:21
Vx.
12:21
Looks good.
12:22
It's going down to zero.
12:26
And it should.
12:28
Vy should be going to a terminal velocity of 44 meters per second.
12:38
So vy, let's put a minus in here again.
12:59
That just increases.
13:02
Is it ever going to decrease? nope.
13:24
Okay, but it has to decrease...