- Good morning.
Today we are going to demonstrate
and understand the classic bullet
projectile motion experiment.
- [Bo] Hey guys.
- [Billy] Hey Bo.
- [Bobby] Hi Bo.
(singing flipping physics)
- Bobby, could you please read the problem?
- One bullet is fired horizontally and simultaneously,
a second bullet is dropped from the same height.
Neglecting air resistance and assuming
the ground is level, which bullet hits the ground first?
- As you can see from the video, rather
than using bullets, we are going to use
a lacrosse ball, which will yield the same
results and will cost a lot less money.
So, we have one lacrosse ball that is dropped
and simultaneously a lacrosse ball that is launched
horizontally both from the same height which
we are going to identify as h.
The basic idea here is that we need to solve for the
changes in time for both bullets.
And in order to do that we need to list the variables
that we know in the y-direction for both cases.
Bo, could you please begin doing that?
- The displacement in the y-direction for both is h.
- (cough) negative, (cough) negative.
- Yeah, negative h because they're both going down.
- And to notice that this is the same for both the one
that was dropped and the one that was launched horizontally.
Bobby, what else do we know?
- The initial velocity in the y-direction is zero for both.
- Yes, regardless of the fact that the one
that was launched horizontally has a velocity
in the x-direction, it still, just like the one
that was dropped, has an initial velocity
in the y-direction that is equal to zero.
Billy, what else do we know?
- Both are in free fall in the y-direction
so their acceleration in the y-direction is negative
nine point eight one meters per second squared.
- Actually I'm going to leave it as negative little g
or the acceleration due to gravity because
I want to point out that that this
is true on any planet not just planet Earth.
Now, notice that three of our uniformly accelerated
motion variables are the same.
Therefore, class, if three of the UAM variables
are the same, what do you think is true of the other two?
- [Class] They are the same.
- Yeah, the same.
- Correct, if three of the UAM variables are the same
then so are the other two UAM variables.
More specifically, in this equation you can see
that the velocity final in the y-direction will be
the same and in this UAM equation you can see
that the change in time will be the same.
Therefore, both will land at the exact same time.
Let's go see the proof of this in the video.
You can see that they both hit the ground
at the same time and, in fact, if we slow
it down enough and go frame by frame,
you can see that they actually are
at the same height at the same time as well.
Again, because in the y-direction, all the uniformly
accelereated motion variables are the same.
- [Billy] Wait a second, right before they hit the
ground isn't the one that was launched horizontally
moving faster than the one that was dropped?
- [Mr. P.] Actually Billy yes, that is correct.
- But didn't you just say that they have
the same final velocity in the y-direction?
- Yeah they do Billy, it's just that the one
that was launched horizontally also has a
velocity in the x-direction, so the final speed
or the magnitude of the final velocity
will be the hypotenuse of the triangle.
- And the hypotenuse of a triangle is always
longer than either of the two sides.
- Oh yeah, I get it now.
Thanks.
- Yes, they have the same final velocity in the
y-direction, however, because the one
that was launched also has a final velocity
in the x-direction, it will then have
a magnitude final velocity which will be greater
than the final velocity in the y-direction.
The magnitude of which is the final
velocity for the one that is dropped.
Quick review.
Because three of the UAM variables are the same,
the change in time is going to be the same,
therefore, both will land at the same time
and the final velocity in the y-direction
will be the same, however, the one
that was launched horizontally will have a larger
final speed than the one that was dropped.
Thank you very much for learning with me today.
I enjoyed learning with you.