1. Projectile Motion
2-D Motion

2. What do you think?
Suppose two coins fall off of a table simultaneously. One coin falls straight downward. The other coin slides off the table horizontally and lands several meters from the base of the table.
Which coin will strike the floor first?
Explain your reasoning.
Would your answer change if the second coin was moving so fast that it landed 50 m from the base of the table? Why or why not?
When asking students to express their ideas, you might try one of the following methods.
(1) You could ask them to write their answers in their notebook and then discuss them.
(2) You could ask them to first write their ideas and then share them with a small group of 3 or 4 students. At that time you can have each group present their consensus idea. This can be facilitated with the use of whiteboards for the groups.
The most important aspect of eliciting student’s ideas is the acceptance of all ideas as valid. Do not correct or judge them. You might want to ask questions to help clarify their answers. You do not want to discourage students from thinking about these questions and just waiting for the correct answer from the teacher. Thank them for sharing their ideas. Misconceptions are common and can be dealt with if they are first expressed in writing and orally.
Many students will respond that the coin falling straight down will strike first because it travels less distance (or for some other reason).
After students answer the questions, you may wish to show them the following demonstration with two quarters. (Practice a few times before class.) Place one quarter so that it extends halfway over the edge of a table, and then place the second coin next to it. Flip the second coin with your finger so it just brushes the first coin. One coin will fall nearly straight down while the other lands far out from the base of the table. Have students remain quiet so that they can hear the coins striking the floor. Students should hear them hitting at the same time, no matter how far out the second coin lands.
You might extend this analogy to firing a rifle horizontally and dropping a bullet at the same time. It is hard for students to imagine that each strikes the ground at the same time (about 0.5 s after firing).

3. Projectile Motion Projectiles: objects that are launched into the air
Gravity affects the motion
Path is parabolic if air resistance is ignored
Path is shortened under the effects of air resistance
Discuss the wide variety of projectiles.
Tell students that the effect of air resistance is significant in many cases, but we will consider ideal examples with gravity being the only force. The effects of air were not very significant in the coin demonstration (see the Notes on the previous slide), but would be much more significant if the objects were traveling faster or had more surface area.
Use the PHET web site to allow students to study projectile motion qualitatively.
Go to simulations, choose “motion,” and choose then choose “projectile motion.”
In this simulation, you can raise or lower the canon. Start with horizontal launches and note that the time in the air is only dependent on the height, and not on the speed of launch. You can change objects, and you can even launch a car. You also have the option of adding air resistance in varying amounts, as well as changing the launch angle.
Have students determine which launch angles produce the same horizontal distance or range (complimentary angles) and find out which launch angle gives the greatest range (45°). Ask them to investigate the effect of air resistance on these results.

4. Components of Projectile Motion
As the runner launches herself (vi), she is moving in the x and y directions.
Remind students that vi is the initial velocity, so it never changes. Students will learn in later slides that vx,i also does not change (there is no acceleration in the horizontal direction) but vy,i does change (because of the acceleration due to gravity).

5. Analysis of Projectile Motion
Horizontal motion
No horizontal acceleration
Horizontal velocity (vx) is constant.
How would the horizontal distance traveled change during successive time intervals of 0.1 s each?
Horizontal motion of a projectile launched at an angle:
Since the initial velocity is constant, the change in x for each successive time interval (such as 0.1 s) will always be the same. Point out that the ball moves the same distance sideways between successive time intervals.
Many students mistakenly believe that the ball is falling straight down eventually. In fact, it keeps moving sideways at a steady rate in the absence of air resistance. With air resistance, it can eventually reach a point where it is falling nearly straight down.

6. Analysis of Projectile Motion
Vertical motion is simple free fall.
Acceleration (ag) is a constant m/s2 .
Vertical velocity changes.
How would the vertical distance traveled change during successive time intervals of 0.1 seconds each?
Vertical motion of a projectile launched at an angle:
Students should note that the vertical distance increases during each successive time interval.
The equations above are simply equations (2), (5), and (4) from the previous section. You might want to write the “old” equations on the board prior to showing them these “new” equations.

7. Projectile Motion - Special Case
Initial velocity is horizontal only (vi,y = 0).
Point out that these equations are the same as those on the previous slides with vi,y = 0 or a launch angle  = 0.
These equations could be used for the coin as it fell off the table (see the Notes on the first slide of this section) or for an object dropped from an airplane flying at a level altitude.
The previous equations (last two slides) are more general and apply to any projectile.

8. Projectile Motion Summary
Projectile motion is free fall with an initial horizontal speed.
Vertical and horizontal motion are independent of each other.
Horizontally the velocity is constant.
Vertically the acceleration is constant (-9.81 m/s2 ).
Components are used to solve for vertical and horizontal quantities.
Time is the same for both vertical and horizontal motion.
Velocity at the peak is purely horizontal (vy = 0).
The 4th and 5th summary points are essential for problem solving. Emphasize these points now, and return to them as students work through problems.