1. Projectile Motion
October 4, 2016

2. So far, we have studied free fall – the vertical (up/down) motion of an object that only experiences force due to gravity. What if I gave a freely falling object an initial horizontal velocity? Would the horizontal velocity affect the up / down motion of the object?
Watch the Myth Busters compare the rate of falling of a dropped bullet versus a bullet fired from a gun
Watch this
And this
Conclusions?
Horizontal motion does NOT affect vertical motion. We will also see that vertical motion does NOT affect horizontal motion. This means we can solve projectile motion problems by dealing with horizontal and vertical motion separately.

3. Horizontally Launched Projectiles
If a ball rolls along the table with constant horizontal velocity, then the moment it leaves the table, it has the same horizontal velocity with which it rolled along the table and zero vertical velocity.
In the horizontal direction, there are no forces on the motion which means no acceleration.
Horizontal velocity remains CONSTANT.
The ball continues to travel horizontally through the air at exactly the same speed which it was rolling on the table.

4. Horizontally Launched Projectiles
If a ball rolls along the table with constant horizontal velocity, then the moment it leaves the table, it has the same horizontal velocity with which it rolled along the table and zero vertical velocity.
In vertical direction there is gravitational acceleration.
The projectile accelerates downward at exactly the same rate as it would if it were just dropped.
When these two motions are combined - vertical free fall motion and uniform horizontal motion - the trajectory will be a parabola.
click me

5. Horizontal component vx is constant throughout the motion.
Projectiles Launched at an Angle
Often, the projectiles are launched at an angle. To solve the problem, we resolve this initial velocity into its horizontal and vertical components. vy v q vx
Horizontal component vx is constant throughout the motion.
Vertical component vy is decreasing on the way up, becoming zero at the top, and increasing on the way down.
click me
Horizontal component of motion for a projectile is completely independent of the vertical component of the motion. Their combined effects produce the variety of curved paths - parabolas that projectile follow.
Give students a chance to answer the questions in the guided notes re helicopter!

6. The Monkey and the Banana Gun ….
A zookeeper has come up with an ingenious way to feed a monkey … using a banana gun!
The problem?
The poor monkey gets scared by the sound of the gun and falls out of the tree the moment the gun goes off.
Knowing this, should the zookeeper aim the banana gun directly at the monkey, slightly below the monkey, or slightly above monkey?
Why?
First, let’s consider if there was no gravity …
Where should the zookeeper aim?
In first slide, describe the problem: the monkey is easily startled, and will let go of the branch the moment the gun is fired. Where to shoot the gun?

7. The Monkey and the Banana Gun ….
In a gravity – free environment
The zookeeper should aim the gun directly at the monkey!
The banana will travel in a straight line (no parabola!) because there is no force (gravity) to change the motion of the banana.
Notice, the monkey also doesn’t fall!
But what if we do have gravity?
Where should we aim then?
In first slide, describe the problem: the monkey is easily startled, and will let go of the branch the moment the gun is fired. Where to shoot the gun?

8. The Monkey and the Banana Gun ….
With gravity!
The zookeeper should aim the gun directly at the monkey!
The monkey falls … but so does the banana! Both fall at the same rate because all objects experience the same acceleration due to gravity!
But wait, doesn’t the speed of the banana matter? What if we had a really slow banana gun?
In first slide, describe the problem: the monkey is easily startled, and will let go of the branch the moment the gun is fired. Where to shoot the gun?

9. The Monkey and the Banana Gun ….
With gravity and a slow gun!
The zookeeper should aim the gun directly at the monkey!
It doesn’t matter if the gun is fast or slow! With a slow gun, both the banana and the monkey will fall a lot before the banana reaches the monkey …
But they still fall at the same rate because …
In first slide, describe the problem: the monkey is easily startled, and will let go of the branch the moment the gun is fired. Where to shoot the gun?
All objects fall with the same acceleration due to gravity!
In other words, the zookeeper should always aim directly for the monkey!

10. Check Your Understanding -- The Truck and The Ball
Imagine a pickup truck moving with a constant speed along a city street. In the course of its motion, a ball is projected straight upwards by a launcher located in the bed of the truck. Imagine as well that the ball does not encounter a significant amount of air resistance.
Where will the ball land?
In front of the truck, 2) In the truck, 3) Behind the truck,
4) We need to know the velocity of th e truck and ball to answer
How do you know?

11. Check Your Understanding -- The Truck and The Ball
Imagine a pickup truck moving with a constant speed along a city street. In the course of its motion, a ball is projected straight upwards by a launcher located in the bed of the truck. Imagine as well that the ball does not encounter a significant amount of air resistance.
Where will the ball land?
In front of the truck, 2) In the truck, 3) Behind the truck,
4) We need to know the velocity of th e truck and ball to answer
How do you know?

12. This is our only new equation!
Range of Projectile Motion (when starting and ending height are equal)
R = 2 vi2 sinθ cos θ
the same range is obtained for two projection angles that add up to 900
750
600
Projectile thrown with the same speed at 300 and 600 will have the same range. The one at 300 remains in the air for a shorter time.
450
300
This is our only new equation!
150
What if we have air resistance?
Air resistance shortens the range of the object, and the path is no longer a parabola. You won’t need to mathematically solve this, but you DO need to be able to describe how air resistance affects the motion.
IDEAL PATH
ACTUAL PATH

13. Check your understanding
If a projectile launches and lands at the same height, what affects how far it travels?
Initial speed and angle
What affects how long a projectile stays in the air?
Height of launch relative to landing, and the
vertical component of initial velocity.

14. Check your understanding
How does a projectile’s vertical velocity change over time?
It becomes more negative.
How does a projectile’s horizontal velocity change over time?
It doesn’t change (if air resistance is ignored)
How does a projectile’s acceleration change over time?
It doesn’t change (always 9.81 m/s2 down)