1. Projectile Motion Or “Fly me to the Moon” Standards:
1i* Students know how to solve two-dimensional trajectory problems.
1j* Students know how to resolve two-dimensional vectors into their components and calculate the magnitude and direction of a vector from its components.

2. Projectile
A projectile is an object that once given an initial velocity moves only under the influence of gravity.
Examples: bullets, baseballs, cannonballs, divers, golf balls, basketballs, volleyballs, footballs, fountains, car flying off cliff
Anti-examples: Rockets when engines are on, airplanes when under power, car on road
all have force acting besides gravity
Question: What is a projectile? Give some examples of projectiles. Give an example of an object which is not a projectile.
Activities:
State that projectile is an object that once given an initial velocity moves only under the influence of gravity.
List examples of projectiles if we neglect air resistance.
List anti-examples and point out outside forces acting besides gravity.

3. Perpendicular Motion Vectors are Independent
The horizontal motion of a projectile does not effect the vertical motion of the same projectile.
Examples
2D apparatus demo
Two bullet problem
Question: What effect does the horizontal motion of a projectile have on its vertical motion?
Activities:
1) Show 2D projectile motion apparatus demo. Point out that we are not saying that both balls travel the same overall distance. Rather they travel the same vertical distance.
2) Show Mythbusters video on two bullet problem
3) State that we’ve shown that horizontal velocity does not affect vertical velocity, distance or acceleration and visa versa

4. Horizontal Projectile
Horizontal motion is one of constant speed
DD=v0Dt
Vf=v0
A=0
Vertical motion is one of freefall
DD=1/2 ag Dt2
Vf=ag Dt
Ag=-10m/s/s
Question: Describe the vertical and horizontal motion of a horizontally projected object. Include in your description how the distance the object travels, the speed and the acceleration changes in consecutive time intervals. Write the equations for distance, speed and acceleration in the the vertical and horizontal directions. Calculate the velocity and distance for an object thrown horizontally at 5 m/s one,two ,three, four and five seconds after it is released. Draw the d-t,v-t and a-t graphs for this situation.
Activities:
Show picture on slide and use white board marker to draw vertical and horizontal distances ball moves. Have class note that horizontally the distances are the same whereas vertically they increase. Ask what model of motion the motion in the vertical and horizontal direction match and write on board that the horizontal motion is that of constant velocity and the vertical motion is that of constant acceleration, namely freefall.
Write distance, velocity and acceleration equations for each direction on board. Point out that velocities are instantaneous and have written the acceleration of gravity as -10 m/s/s.
Summarize that what we’ve found is that if you split up the motion of the projectile into horizontal and vertical motion, the vertical motion turns out to be free fall and the horizontal motion is constant velocity. Thus we can use the two models of motion we learned last week. In other words, all the equations and freefall numbers from last week still apply. We have divided and conquered!

5. Check Question 1
A cannon sits on a 80 m high cliff. If a cannon ball is projected horizontally with an initial velocity of 10 m/s answer the following questions.
What are the horizontal speed and distance traveled of the ball after 3 seconds?
What are the vertical speed and distance traveled of the ball after 3 seconds?
When does the ball hit the ground?
How far away from the cliff does the ball hit?

6. Projectiles Launched at Angles
Decompose initial velocity vector
Vertical equations
DDy=v0yt + 1/2 ag Dt2
Vfy=v0y+ag Dt
Vfy 2 =v0y 2+2ag Ddy
(vfy +v0y) / 2 =Ddy
Horizontal Equation
Ddx=v0x Dt
At top Vy=0, Vx=Vox, a= -10 m/s/s, max range at 45 degrees
Question: How does shooting the projectile up change the kinematic equations used for a projectile? How do you determine how much of the initial velocity is in the vertical and horizontal directions? Should the gravity terms be positive or negative if the projectile is shot upward? How about the initial velocity in the vertical direction?
Activites:
Discuss how to break up initial velocity into its components. Discuss picking origin and positive directions.
Show upward projectile picture on slide. Discuss no gravity path and then add gravity to come up with true trajectory. Write equations for horizontal and vertical directions.
Make a time-velocity and time distance table for the y or vertical direction. Ask for how far and how fast numbers for gravity. Now show what initial y velocity numbers do to numbers and point to graph showing how the math confirms the picture.
Make a time velocity and time distance chart for the x or horizontal direction. Again show that this confirms the picture we’ve seen.
Show downward projectile picture on slide. Discuss no gravity path and then addition of gravity. Write equations for vertical and horizontal directions.
Discuss boundary conditions at top of upward shot projectiles trajectory. Mention that with no air resistance, 45 degrees will give the greatest range. Initial velocity in y direction determines time in air which leads to common practice of finding t with one of the vertical equations and then using it to find the horizontal range.
Briefly mention shooting downward and how y values would change but x values would remain same.
Finish with the Alf demonstration.

7. The Monkey Shot
If monkey does not let go then need to aim above monkey.
If monkey lets go at same time as bullet shot then aim directly at monkey
Bullet and monkey will fall at same rate
Bullet will fall off straight line no gravity path
Do Alf Experiment

8. Summary Slide
Projectiles are objects which once given an initial velocity move under the influence of gravity only (neglecting air resistance).
The vertical and horizontal components of motion are independent of one another.
The horizontal motion of a projectile is that of an object with a constant speed. The vertical motion is that of an object undergoing a constant acceleration.
Demo: Alf Experiment

9. Upward Projected Object
Decompose initial velocity
Horizontal motion is constant velocity.
D=v0x Dt, a=0
Vf=v0x
Vertical motion is difference between motion due to initial speed and freefall
DDy=v0y Dt - 1/2 ag Dt2
Vfy=v0y-ag Dt
Vfy 2 =v0y 2-2ag Ddy
(vfy +v0y) Dt / 2 =Ddy
Question: How does shooting the projectile up change the kinematic equations used for a projectile? How do you determine how much of the initial velocity is in the vertical and horizontal directions? Should the gravity terms be positive or negative if the projectile is shot upward? How about the initial velocity in the vertical direction?

10. Downward Projected Object
Horizontal motion is that of object moving with constant velocity
D=v0x t a=0
Vf=v0x
Vertical motion is sum of motion due to initial velocity and freefall
D=-v0yt - 1/2 agt2
Vfy=-v0y-agt
a=10m/s/s
Question: Describe the vertical and horizontal motion of a downward projected object. Include in your description how the distance the object travels, the speed and the acceleration changes in consecutive time intervals. Write the equations for distance, speed and acceleration in the the vertical and horizontal directions. Calculate the velocity and distance for an object thrown down at 5 m/s one,two ,three, four and five seconds after it is released. Draw the d-t,v-t and a-t graphs for this situation.