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8
volunteer
over the adjacent
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student
Mhm
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volunteer
and the adjacent is gonna 5000. We'll keep it in feet.
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volunteer
And the opposite is always gonna 1000 + 600T.
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volunteer
Oops, no, I have to reset.
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volunteer
Excuse me here, let me see if I can do it again.
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volunteer
No
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volunteer
I'm sorry
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volunteer
One more time with feeling
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student
So
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volunteer
Let me lengthen this
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volunteer
1000
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volunteer
I can't write very well, 5000.
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volunteer
OK
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student
OK
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volunteer
So if we think about it
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volunteer
iste as the number of seconds that go by. We started at 0.
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volunteer
then the tangent of the angle is going to be 15%, right?
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volunteer
1000 /.
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volunteer
5000
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student
Yeah
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volunteer
As, as each second picks by.
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volunteer
the the tangent of the angle is gonna get bigger and bigger.
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student
Mm
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volunteer
um after 1 2nd, it'll be 1600 over
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volunteer
5000. 2 seconds, it'll be
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volunteer
2200
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volunteer
/5000 and on up, right?
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student
Mm
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volunteer
Does that make sense to you
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student
You mean?
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volunteer
I'm sorry
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student
You mean? What, what did you mean?
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volunteer
OK
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volunteer
So let's, let's just look at this expression.
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volunteer
tangent of the angle = . I, I'm sorry about my writing. It's 1000 + 600T / 5000.
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volunteer
So at time equals 0
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student
Mm.
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volunteer
if T is equal to 0, 600 times 0 is 0, and we would end up 1000 /, 5000, excuse me.
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student
Mhm
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volunteer
If it at time T equals 1 2nd, we would be 1600 /
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volunteer
5000, right?
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student
Yeah
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volunteer
At time T equals 2 seconds, we would be at
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volunteer
2200 / 5000, and so forth.
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student
Yup
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volunteer
So we have a, we now have an expression, if we've done this correctly
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volunteer
of the tangent of the angle
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volunteer
in terms of tea
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volunteer
And that's pretty good because now we can use our
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volunteer
knowledge of derivatives
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volunteer
to find the theta DT.
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student
All right, real quick, can we, can I ask, wait, why, why is it plus and not like times?
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volunteer
It is time
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volunteer
but we're starting out in
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student
Don't 1000 + 600.
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volunteer
Yeah, I'm sorry about my writing. I really apologize.
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volunteer
It's a 1000 + 600T.
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volunteer
Can you see that or
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student
No, I can see that I'm just saying like why is it that way?
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volunteer
OK
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volunteer
So think about that angle
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student
Mhm.
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volunteer
If we're just starting out
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volunteer
do you agree that the angle, the tangent of the angle is 1000 / 5000.
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student
Yes, I agree
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volunteer
OK.
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volunteer
If you, if you plug in T equals 0 into the formula, we would get 600 times 0, right?
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student
Yeah
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volunteer
And we would end up 1000 / 5000 when we're starting.
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volunteer
After 1 2nd
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volunteer
if we just choose an arbitrary value 1 2nd.
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volunteer
what would the numerator be?
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volunteer
if I plug in 1 2nd
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student
led to 1600
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volunteer
adding to 1000, yes, 1000 + 600 times 1 2nd, right?
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student
Yeah
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volunteer
So we would end up 1600, correct?
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student
Yeah, I'll get that part. I'm just saying like the 1000 + 600. Like why is 1000 + 600 and now 1000 times 600.
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volunteer
OK.
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volunteer
So that
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volunteer
we're, we're gonna
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student
or minus 600
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volunteer
we're, we're, the rocket is going up.
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student
Mhm
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volunteer
We have to multiply by the 6 6001 times the tea, if that helps clear that up. So,
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student
Yeah, that part is clear
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volunteer
OK.
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volunteer
So
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volunteer
if you think about where the rocket is vertically.
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volunteer
We can't multiply 600T. It's starting out 1000 ft.
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student
Mm
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volunteer
So we always just start out 1000 ft.
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student
Mhm
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volunteer
and after what, after 1 2nd for for example, we will be 1600 ft. Do you agree with that?
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student
Right
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volunteer
and the way I got that was after 1 2nd
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volunteer
the velocity 600 ft per second.
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volunteer
times the time
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volunteer
is 1 2nd
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