Mr.P.: Good morning.
Today we're going to demonstrate the components
of projectile motion by building
velocity and acceleration vector diagrams.
Bo: Hey guys.
Billy: Hey Bo.
Bobby: Hi Bo.
♫ (lyrics) Flipping Physics ♫
Mr. P.: Let's start with a quick review of projectile motion.
Bobby, please remind me, what is true
of the motion of a projectile in the X-Direction.
Bobby: In the X-Direction, the projectile
will move at a Constant Velocity.
Mr. P.: Correct, in the X-direction
the velocity of a projectile is constant.
Billy, what about the motion
of a projectile in the Y-Direction?
Billy: In the Y-Direction,
a projectile experiences Uniformly Accelerated Motion
with an acceleration equal to the negative
of the acceleration due to gravity.
On Earth, that acceleration would be equal to
-9.81 meters per second squared.
Mr. P.: Yes, in the Y-direction the acceleration is constant
therefore we can use the UAM equations of motion.
Therefore, projectile motion is made up
of a horizontal and a vertical component.
The Horizontal Component is Constant Velocity.
And the Vertical Component is Uniformly Accelerated Motion.
With a downward acceleration that has a magnitude
of 9.81 meters per second squared.
Now, let's combine them all.
Again, notice how the X-direction has a Constant Velocity.
And the Y-direction has a uniform downward acceleration.
Now let's add velocity vector components in the X-direction.
Bobby, what should the velocity vector components
look like the X-direction for the ball
as it moves to the right?
Bobby: Well, in the X-direction
the ball has a constant velocity to the right,
so the vector should have the same magnitude
the whole time and be pointed to the right.
Mr. P.: Correct.
So, as the ball moves to the right
we can freeze the ball at several locations,
and add the velocity vector in the X-direction
which will always have the same magnitude
and therefore the same length arrow.
Now, let's just look at the Upward Motion
of the ball in the Y-direction.
Billy, what should that Velocity Vector look like?
Billy: Well, we know the ball must start
with an upward velocity in the Y-direction.
And because the acceleration is downward,
that velocity will decrease as the ball goes upward.
So the magnitude of the Velocity Vector will decrease.
And it should eventually reach zero at the very top.
Mr. P.: And Bo, what about the velocity vectors
of the ball in the Y-direction as the ball is going downward?
Bo: As Billy pointed out at the very top in the Y-direction
the ball has a velocity of zero.
So the ball will have an initial velocity of zero
and accelerate downward.
So the velocity will have an increasing downward magnitude
as the ball goes down.
Mr. P.: So again in the Y-direction as the ball moves upward
that velocity will be upward and decrease in magnitude
until it reaches zero at the very top.
As the ball moves down.
That velocity will start out at zero,
and increase in magnitude and always be downward.
Now, let's take a look at projectile motion.
Remember, projectile motion is a combination
of the horizontal and the vertical components.
So we can now take those
horizontal and vertical velocity vectors.
And add them to the projectile motion video.
Those velocity vectors are the x and y components
of the resultant projectile motion velocity vectors.
Which we can now add to the video.
And there are all the velocity vectors for projectile motion.
Billy: Wow! That's pretty cool Mr. P.!
Bo: Hold up, Mr. P.
I don't get what you just did
with the velocity vectors in projectile motion.
Bobby: Yeah, can you please explain
how you got those Resultant Velocities?
Mr.P.: Sure, let's take a look
at the initial velocity vectors.
The components of the Initial Velocity look like this.
And we can do tip-to-tail vector addition
to determine the Resultant Initial Velocity Vector.
And you can see we the initial velocity vector right here.
And because of the associative property of vector addition.
We can actually add them in any order.
So let's do it again.
Only this time starting with
the Initial Velocity in the Y-direction.
And we get the same Resultant Initial Velocity Vector.
And we can illustrate that on our original diagram like this.
And you can see we get a rectangle.
A diagonal of which is the Resultant Velocity Vector.
Does that help?
Bo: Yes, thanks.
Bobby: Yeah, I get it now.
Mr. P.: Good.
Now, I do want to add acceleration to the picture as well.
So, on the projectile motion video,
let's remove all the velocity vector components.
And just leave the Resultant Velocity.
Now, what about acceleration?
Bobby, what do you know about
the acceleration of a projectile in the Y-direction?
Bobby: The acceleration is constant
at 9.81 meters per second squared downward the whole time.
Mr. P.: The whole time?
Even when the ball is going upward?
Bobby: Uh, yes even when a projectile is moving upward
its acceleration is still downward and constant.
Mr.P.: Very good, Bobby.
So now we can add a constant downward acceleration
to both the upward and downward moving projectiles.
Now, Billy, what about the acceleration
of the ball moving in the X-direction.
Billy: Because the ball moves
at a constant velocity in the X-direction,
the acceleration in the X-direction is zero.
Mr.P.: Yes, and we illustrate that in the diagram
by, well, not adding anything.
Which means that the net acceleration
is just acceleration in the Y-direction
which we can now add to projectile motion video.
And that is a visual description of the velocity
and acceleration components
of an object in projectile motion.
(airy celestial music)
There you have it.
We just demonstrated the horizontal
and vertical components of projectile motion.
By building velocity and acceleration vector diagrams.
Thank you very much for learning with me today.
I enjoyed learning with you.