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We now know how long the object
is going to be in the

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air, so we're ready to
figure out how far

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it's going to travel.

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So we can just go back to kind
of the core formula in all of

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really kinematics, all of kind
of projectile motion or

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mechanical physical problems,
and that's distance is equal

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to rate times time.

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Now, we're talking about the
horizontal distance.

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So our distance is going to be
equal to-- what's our rate in

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the horizontal direction?

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We care about horizontal
distance traveled, so our rate

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needs to be the horizontal
component of the velocity, or

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the magnitude of the horizontal

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component of the velocity.

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And we figured that out
in the first video.

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That is s cosine of theta.

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So let's write that
down right here.

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So our rate is s cosine
of theta.

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And how long will we
be traveling at

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this horizontal speed?

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Well, we'll be going at
that speed as long as

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we are in the air.

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So how long are we in the air?

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Well, we figured that out
in the last video.

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We're going to be in the air
this long-- 2 s sine of theta

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divided by g.

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So the time is going to be
2 s sine of theta over g.

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So the total distance we're
going to travel, pretty

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straightforward, rate
times time.

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It's just the product
of these two things.

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And we could put all of the
constants out front, so it's a

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little bit clearer that it's
a function of theta.

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So we can write that the
distance traveled-- let me do

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that same green.

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The distance traveled as a
function of theta is equal

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to-- I'll do that
in this blue.

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This s times 2s divided by g
is-- I'll do it in a neutral

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color actually.

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This s times 2s divided by g is
2 times s squared over g.

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So 2s squared over g times
cosine of theta

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times sine of theta.

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So now we have a general
function.

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You give me an angle that I'm
going to shoot something off

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00:02:23,830 --> 00:02:28,540
at and you give me the magnitude
of its velocity, and

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00:02:28,540 --> 00:02:30,860
you give me the acceleration
of gravity.

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I guess if we were on some
other planet, who knows?

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00:02:33,620 --> 00:02:35,350
And I will tell you
exactly what the

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horizontal distance is.

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