Projectile Motion…it’s as easy as rolling off a cliff…

Prediction

Before you participated in the PhET simulation, you made a prediction and explained your reasoning to me via email.

A Little History…

A few years ago, researchers went to elementary, middle, and high schools as well as universities and showed students this image and asked them,

“Ignoring air resistance, which of the following correctly shows what an object would do if it rolled off a cliff?”

The Results The breakdown of answers they got was almost exactly

the same at all ages.

About 60% said “A” was correct. The object will stop in midair, and then start to fall straight down. Because some people referred to the coyote in cartoons, the researchers called it the Wile E. Coyote Effect.

About 25% said “B” was correct. The object will move forward at first, but will eventually just fall straight down.

About 15% answered “C”. The object will continue to move forwards the entire time it is falling.

So What’s the Correct Answer?

I’m not going to tell you. We’ll revisit the question at the end of these notes.

Observations from the Simulation

As we saw with the simulation, the projectile that fell straight down and the one that was shot from a cannon horizontally - hit the ground in the same amount of time.

So what effect did horizontal velocity have on the time it took (the downward motion of) the projectile to hit the ground? None!

The best conclusion we can make from this is that the horizontal motion of a projectile does not affect downward motion of the projectile.

Observations from the lab

Intuition will tell you that the horizontally launched object will “hang” in the air.

But… YOUR INTUITION (at least in this case) IS WRONG!

Here’s a video Here’s another video

Horizontal and Vertical Motion

The most important thing you can remember about projectile motion is this:

Horizontal and Vertical motion are completely, 100% INDEPENDENT of each other – even when they are happening at the same time.

Your lab question was, “How does initial velocity affect the amount of time it takes a horizontally-launched object to reach the ground?”

Does Horizontal Affect Vertical?

The short answer to the lab question is: It Doesn’t! The horizontal motion of the projectile is

unaffected by the downward (vertical) force of gravity.

What does affect how long it takes an object to hit the ground (ignoring air resistance)? One thing and one thing only… The height it is launched from!

Looking at velocity vectors On the next slide, we’re going to look at the paths

two projectiles follow. One projectile is shot out of a cannon, the other is dropped at exactly the same moment.

yes, just like the lab

When going through the slide, remember: velocity is a vector (has magnitude & direction) gravity is a constant force constant forces cause acceleration

While clicking through this slide, keep in mind that the law of inertia tells us that objects in motion stay in motion at a constant speed and in a straight line. Since horizontal motion is independent of vertical motion, the horizontal vector never changes!

two cannon balls – one is given a horizontal force, the other is just dropped

gravity acts downward on both

horizontal motion continues

gravity is a constant force that accelerates all falling objects (ignoring air resistance)

gravity acts on all objects equally

Back to the cliff…So…which path will the red ball travel?

It will follow path C – because its horizontal motion will continue at the same speed and direction (law of inertia) while gravity exerts a downward force at the same time!

Reflection

As we saw with the ball and the cliff question, many people – even highly educated people – have misconceptions about falling objects versus objects with a high horizontal velocity.

Ask five of your friends or family members which bullet will stay in the air longer: one shot from a pistol or one dropped from pistol height. (Obviously, don’t ask students in this class or physics majors )

Reflection On the discussion board page, join the discussion

about why you think most people have the misconception that a bullet fired from a gun will “hang” in the air. What is it about a bullet from a gun (or an arrow from a bow and arrow, or a cannon ball out of a cannon, etc.) that makes it so hard to believe that gravity acts on it exactly the same way gravity acts on an object with no horizontal velocity (ie, one that is dropped)?

Make one original post and respond to at least two other student’s posts.