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Welcome back.
Well, I just-- hopefully, we together figured out correctly
that the total time in the air is this initial velocity in
this direction divided by 10.
That's our total time in the air.
And now, how far is the object going to go?
Well it's going to go, our displacement or our distance
in this x direction is going to be-- so, let's see, We
could call it distance in the x direction is going to be
equal to vx, this vx times time.
Times time in the air, right?
Times this number.
And this is the average velocity
because it's not changing.
This is a constant.
Assuming we have no friction or no air resistance-- air
resistance is really just a form of friction.
The horizontal component of this velocity is going to stay
the same the entire time.
So the total distance traveled is going to equal this number.
Let me switch back to that purple, so you
know what I'm doing.
v sub i square root of 3 over 2.
That's this times the time in the air.
Well the time in the air is this.
Times v sub i over 10.
So the distance total traveled-- let's see.
Let's multiply these.
vi squared times the square root of 3, all
of that over 20.
So now we know as a function of our initial velocity in
this direction, how far is this thing going to travel?
Well we know that we want it to travel exactly 100 meters.
So we just set them equal to each other.
We say 100 is equal to vi squared times the square root
of 3 over 20.
And then we can multiply both sides times
the inverse of this.
We could multiply both sides by 20 and divide by the
square root of 3.
So we get v sub i squared is equal to-- let me see.
20 times 100 is 2,000, divided by the square root of 3.
So it's 2,000 times the square root of 3.
And so our initial velocity we need to shoot this thing at is
going to be the square root of this.
So initial velocity is going to be the square root of 2,000
divided by the square root of 3.
So let's figure out what that number is, just to give us a
sense of whether this feels right.
Let me take the square root of 3 first. 3 square root.
And let me inverse that times 2,000.
That equals 1154.7 and then I can square root this.
33.98.
So almost 34 meters per second.
So my initial velocity has to be 33.98 meters per second for
me-- so my initial velocity has to be 33.98 meters per
second to exactly hit this target 100 meters away.
I think that is fairly cool.
And we could also do it to figure out-- you know, we
could do it backwards to figure out if we know exactly
what our velocity is going to be, maybe like a slingshot--
always has the same velocity and the only thing I can
change is the angle.
As long as we know our inverse trigonometric functions, we
can actually figure out the exact angle that we have to
aim the slingshot or the catapult or whatever to hit
the target.
So I don't want you to go out and raise your own army and
then whatever else, but if you have to, you now know how to
command artillery.
With that, I will leave you.
And hopefully, you will not do something overly destructive.
I'll see you soon.