1. What is Projectile Motion?

2. Projectile Motion Two-dimensional motion of an object Vertical
Horizontal

3. Projectiles
Airborne objects that move as a result of their own inertia and gravity.
They exhibit two dimensional motion.
Horizontal and vertical motion
Horizontal and vertical motion are independent of one another.
The resultant motion is a combination of horizontal and vertical motion.

6. Types of Projectile Motion
Horizontal
Motion of a ball rolling freely along a level surface
Horizontal velocity is ALWAYS constant
Vertical
Motion of a freely falling object
Acceleration due to gravity
Vertical component of velocity changes with time
Parabolic
Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity

7. Components of Projectile Motion
Projectiles have:
vertical velocities that increase and decrease because they are influenced by gravitational forces.
horizontal velocities remain constant because they are not influenced by gravitational forces.

8. Examples of Projectile Motion
Launching a Cannon ball

10. Two Dimensional Horizontal Motion for Projectiles
Horizontal displacement “x” is called the range.
d = v1t x = vt
Assume v1 does NOT change.
So v1 = v2 therefore the acceleration in the x or horizontal direction is always zero.

11. Two Dimensional Vertical Motion for Projectiles
Displacement in the “y” is called the height.
Assume the acceleration is -9.8 m/s2
Assume v1 is zero
d=1/2 at y = ½ at2
V22 = 2ad V22 = 2ay
V2 = at V2 = at

12. Factors Affecting Projectile Motion
What two factors would affect projectile motion?
Angle
Initial velocity
Initial Velocity
Angle

13. Class Exercise
An object is fired from the ground at 100 meters per second at an angle of 30 degrees with the horizontal
Calculate the horizontal and vertical components of the initial velocity
After 2.0 seconds, how far has the object traveled in the horizontal direction?
How high is the object at this point?

14. Solution
Part a
Part b
Part c

15. Two Types of Projectiles

16. Steps to working a problem
Draw the picture
Label with variables and numbers
Write the givens
Write what you are looking for
Write equation
Plug and chug
Answer with number and unit!

17. Anytime an object starts at an angle from the ground!
Vy at the highest peak is always 0
Remember when use max height and Vy=0….it’s only half the time the object stays in the air
So…to find total distance (dx)…multiply time by 2

18. Anytime the object starts at a given height
Do not multiply time by 2….since starts at max height already

19. A. Maximum height of projectile B. Launch Velocity C. Launch angle
EX 1: A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate …
… note – think of various ways this question could be formed on a test (cannon fires, football thrown, baseball hit, golf ball hit, soccer ball kicked, etc.)
A. Maximum height of projectile
B. Launch Velocity
C. Launch angle

20. A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate …
A. Maximum height of projectile.
Answer …
Begin with equation
Use the fact that at top of trajectory Vyi is zero. And use second half of trajectory.
Formula simplifies to
Plugging in values:

21. A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate …
B. Launch Velocity.
Answer …
Need X and Y velocities (Vavg.x and Viy). Launch velocity is found using Pythagorean theorem.
Vx is found using:
Viy is found using half of trajectory and:
Knowing that Vfy is zero at half the time …
So …

22. Use triangle and trig function. So
A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate …
C. Launch Angle.
Answer …
Use triangle and trig function. So θ

23. Ex 2:An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate …
… note – think of various ways this question could be applied (dropped from a moving vehicle, dropped by a flying object, rolls off a cliff, rolls off a table, etc.)
A. Velocity of object

24. An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate …
A. Velocity of object.
Answer:
Typical to these types of problems, first step would be to find the time in the air (fall time). This is found using the vertical distance (dy).

25. An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate …
Velocity of object.
Answer:
Then use time (8.45 s) with X distance (dx) to calculate horizontal velocity (Vx).

26. Ex 3: An object is travelling at 37◦ with an initial velocity 8 m/s
Ex 3: An object is travelling at 37◦ with an initial velocity 8 m/s. How long will it take to go 38 m horizontally?
… note – think of various ways this question could be applied (boat/swimmer crossing river, airplane, ball thrown from vehicle, etc..)

27. Need X component velocity. Answer:
An object is travelling at 37◦ from vertical at velocity 8 m/s. How long will it take to go 38 m horizontally?
Need X component velocity.
Answer:
Note that (similar to projectiles) time is shared between two motions. Each component is independent of the other.
θ=37

28. Review Questions
In the absence of gravitational force and friction, describe the motion of an object.
How do you describe horizontal motion?
Is vertical motion influenced by gravitational force?
How far is an object being thrown horizontally given an initial speed of 20 m/s from a 45 m tower?