Projectile Motion (Finding through Component methods)

Projectile Motion (Finding through Component methods)

1. Projectile Motion

2. LEARNING OBJECTIVES Define Projectile Motion Explain Projectile Motion Identify the types of Projectile Motion Differentiate the types of Projectile Motion Explain and summarize all the kinematics equation in solving Projectile Motion problems Solve problems involving the types of Projectile Motion

3. What is projectile? Projectile - Any object which projected by some means and continues to move due to its own inertia (mass).

4. Projectiles move in TWO dimensions A projectile moves in 2 - dimensions, therefore, it has 2 components just like a resultant vector.

5. Horizontal “Velocity” Component It NEVER changes, covers equal displacements in equal time periods. This means the initial horizontal velocity equals the final horizontal velocity In other words, the horizontal velocity is CONSTANT. BUT WHY? Gravity DOES NOT work horizontally to increase or decrease the velocity.

6. Vertical “Velocity” Component Changes (due to gravity), does NOT cover equal displacements in equal time periods. Both the MAGNITUDE and DIRECTION change. As the projectile moves up the MAGNITUDE DECREASES and its direction is UPWARD. As it moves down the MAGNITUDE INCREASES and the direction is DOWNWARD.

7. Combining the Components These components produce what is called a TRAJECTORY or path. This path is PARABOLIC in nature. Component Magnitude Direction Horizontal Constant Constant Vertical Changes Changes

8. Horizontally Launched Projectiles Projectiles which have NO upward trajectory and NO initial VERTICAL velocity.

9. Horizontally Launched Projectiles To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction. And for this we use kinematic #2. Remember, the velocity is CONSTANT horizontally, so that means the acceleration is ZERO! Remember that since the projectile is launched horizontally, the INITIAL VERTICAL VELOCITY is equal to ZERO.

10. Horizontally Launched Projectiles Example: A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land? What do I know? What I want to know? v ox =100 m/s t = ? y = 500 m x = ? v oy = 0 m/s g = -9.8 m/s/s 10.1 seconds 1010 m

11. Vertically Launched Projectiles Component Magnitude Direction Horizontal Constant Constant Vertical Decreases up, 0 @ top, Increases down Changes Horizontal Velocity is constant Vertical Velocity decreases on the way upward Vertical Velocity increases on the way down, NO Vertical Velocity at the top of the trajectory.

12. Vertically Launched Projectiles Since the projectile was launched at a angle, the velocity MUST be broken into components!!! v o v ox v oy q

13. Vertically Launched Projectiles There are several things you must consider when doing these types of projectiles besides using components. If it begins and ends at ground level, the “y” displacement is ZERO: y = 0

14. Vertically Launched Projectiles You will still use kinematic #2, but YOU MUST use COMPONENTS in the equation. v o v ox v oy q

15. Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (a) How long is the ball in the air? (b) How far away does it land? (c) How high does it travel? v o =20.0 m/s q = 53

16. Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (a) How long is the ball in the air? What I know What I want to know v ox =12.04 m/s t = ? v oy =15.97 m/s x = ? y = 0 y max =? g = - 9.8 m/s/s 3.26 s

17. Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (b) How far away does it land? What I know What I want to know v ox =12.04 m/s t = 3.26 s v oy =15.97 m/s x = ? y = 0 y max =? g = - 9.8 m/s/s 39.24 m

18. Sample problem: A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (c) How high does it travel? CUT YOUR TIME IN HALF! What I know What I want to know v ox =12.04 m/s t = 3.26 s v oy =15.97 m/s x = 39.24 m y = 0 y max =? g = - 9.8 m/s/s 13.01 m

19. BASICS STUDENTS should know What is a Projectile Motion? What is a Projectile? What is a Trajectory? Why is Horizontal Velocity is constant all throughout in Projectile Motion? Why is Vertical velocity is zero at maximum height? What is changing in Projectile Motion? What is the difference between Half Projectile Motion and Full Projectile Motion? What is the difference Half-Time and Hang-Time? Is there an acceleration along the horizontal in Projectile Motion? Is there an acceleration along the vertical in Projectile Motion? What is it?

20. Half projectile motion

21. FULL PROJECTILE MOTION

22. Projectile motion HORIZONTAL a x = o, V ox =V x = constant Half projectile: R= V ox t Full Projectile: X = Xo + V ox t R = V ox T VERTICAL Half Projectile: Voy =0 Y=1/2 ag t², use a g = -9.8 m/s² Full Projectile: @max pt / ht : Vy =0, use a g = -9.8 m/s² Y = Yo + V oy t + ½ agt²

23. OTHER KINEMATICS EQUATIONS TO BE USED IN PROJECTILE MOTION Vox = Vo cos ø V oy = Vo sin ø V = √Vx² + Vy² Ø = tanˉ­¹ ( Voy /Vox) or Vy / Vx Vy² = Voy² + 2 a g Y Vy = Voy + agt

24. More examples A slingshot is used to launch a stone horizontally from the top of a 20.0 meter cliff. The stone lands 36.o meters away. a. At what speed was the stone launched? (17.82 m/s) b. What is the speed and angle of impact? ( 26.64 m/s, -47.98 degrees) 2. A cannon fires a cannonball 500.0m downrange when set at 45 degree angle. At what velocity does the cannonball leave the cannon? (Answer: 70.0m/s)

25. evaluation 1. A punter in a football game kicks a ball from the goal line at 60 degrees from the horizontal at 25.0 m/s a. What is the hang time of the punt? (Ans: 4.41 s) b. How far downfield does the ball land? (Ans: 55.2m) 2. A skier leaves the horizontal end of a ramp with a velocity of 25.0m/s and lands 70.0 m from the base of the ramp. How high is the end of the ramp from the ground? (Answer: 38.5 m)

26. ASSIGNMENT Study in advance about Newtons Law of Motion

27. QUOTE TO LIVE BY… “Project, launch yourself and be discovered…” - YOURS TRULY-