Is this possible?

1. Explain your reasoning Is this possible?

2. Unit 3 Projectile Motion

3. Objectives • LT3A- Recognizean object as a projectileLT3B- Predict the motion of a projectile launched horizontally in terms of the horizontal and vertical components of the motionLT3C- Calculate the horizontal and vertical components of a vectorLT3D-Calculate the range, time of flight, initial velocity, and impact velocity of a projectile launched horizontallyLT3E- Predict the motion of a projectile at some angle in terms of the horizontal and vertical components of the motionLT3F- Analyze and calculate horizontal and vertical components of a vector using trigonometric functionsLT3G- Solve projectile motion problems representing the relationship between projection angles, velocity, time of flight, range, and impact velocity.

4. Projectile Motion • A projectile is any object that is projected by some means and continues in motion by its own inertia. • The velocity of a projectile has a horizontal and verticalcomponent. Each component acts independently of the other!

5. Projectile MotionDiagram and Symbols • Vi = initial velocity height (dy) or ymax • Vy,i = initial vertical • velocity vi Vy,i Vx,i • Vx,i = initial horizontal • velocity Range (dx)

6. Where do we see projectile motion? • http://www.youtube.com/watch?v=T9Kl6OtWZIc&feature=relmfu • http://www.youtube.com/watch?v=WaIWJfqDkwY&NR=1&feature=fvwp

7.  = launch angle (from the horizontal) Vy Vi Vy  • For the vertical motionthe acceleration is -9.8m/s2 (or 9.8 m/ s2 downward). Vy = Vi• sin  g = -9.8m/s2 • For the horizontal motion there is NO acceleration. Vy =Vi• cos 

8. Projectile Motion • The shape of a projectiles path is a parabola. • Maximum range for a projectile is achieved with a projection angle of 45°.

9. Does this theory hold? • At the instant a horizontally held rifle is fired, a bullet held at the rifle’s side is released and drops to the ground. Which bullet strikes the ground first, the one fired from the rifle or the one dropped?

10. In the presence of air resistance, the trajectory of a high-speed projectile falls short of a parabolic path. • A projectile fired horizontally will hit the ground at same time as an object… • …dropped from rest if they are released at the same height. • Demo: Ball projection and drop

11. What do you think? • http://www.youtube.com/watch?v=D9wQVIEdKh8&feature=related

12. Horizontal Motion and Freefall • The ball’s horizontal component remains constant. B/c there is no horizontal force acting on it. • Once in flight the only force on the ball is gravity working in the vertical direction. • Both balls fall the same vertical distance in the same time. Vertical distance has nothing to do with Horizontal component of motion. • Downward motion of projected ball is the same as that of free fall.

13. Horizontal Motion • Green: Absence of gravity, constant velocity • Blue: Free fall • Red: Horizontal projection in presence of gravity, horizontal vel. Is not altered. Distance and time are the same. • The vertical force acts perpendicular to the horizontal motion and will not affect it since perpendicular components of motion are independent of each other. Thus, the projectile travels with a constant horizontal velocity and a downward vertical acceleration.

14. Example Question • If the snowmobile is in motion and launches the flare and maintains a constant horizontal velocity after the launch, then where will the flare land (neglect air resistance)? • a. in front of the snowmobile • b. behind the snowmobile • c. in the snowmobile

15. Example Question • Suppose an airplane drops a “pleasant” package while it is moving with a constant horizontal speed at an elevated height. Assuming that air resistance is negligible, where will the relief package land relative to the plane? • a. below the plane and behind it. • b. directly below the plane • c. below the plane and ahead of it

16. Example Questions • You are driving along in an open car and throw a ball straight up into the air. Neglect air resistance. (a) Where does the ball land relative to the car? Answer: In the car.

17. (b) While the ball is still in the air you step on the accelerator. Where does the ball land relative to the car? Answer: Behind the car. (c) What if you stepped on the brake instead? Answer: In front of the car.

18. Example Questions • You drop a ball from the window of a school bus moving a 10 miles/hour. Neglect air resistance. (a) Where does the ball land relative to your hand? Answer: Directly below your hand.

19. (b) What is the shape of the path made by the ball seen by someone outside the bus? Answer: A parabola.

20. Summarizer • What is a projectile? • What is the acceleration of a horizontally projected object in both the vertical and horizontal directions? • Why will a projectile fired horizontally hit the ground at the same time as an object dropped from rest if they are released at the same height?

21. Projectile Motion Equations Kinematic Equations Ymax = maximum vertical displacement Vy = final velocity at a given time in y-direction Vyi = initial velocity in y-direction Vx = final velocity in x direction Vxi = initial velocity in x-direction dx = total horizontal displacement g = acceleration due to gravity t = time

22. Problem Solving Follow these steps to solve problems: Read Problem Make Diagram Identify Knowns Identify Unknowns Choose Formula Solve (and Check) Acronym R.D. KUFS (Mr. Hairston’s Rap Alias)

23. Horizontal Projection • Once the cannon ball leaves the cliff, it experiences a downward acceleration equal to gravity. • Thus the vertical velocity (Vy) is continually increasing. • The horizontal velocity (Vx) remains constant and is equal to Vxo. • The two vectors Vx and Vy are added together to get the velocity at instantaneous points on the path. • When an object is shot horizontally from the same height, but with different force, it will always take the same amount of time to land. The bigger the initial force, the farther the object will travel, but they will all land at the same time.

24. I DO • A cannon shoots a cannon ball horizontally from a 24m high cliff, which lands 100m from the base of the cliff. • a. With what velocity was the projectile fired? • b. What is the projectiles velocity as it strikes the ground?

25. WE DO • A golf ball is projected with a horizontal velocity of 30 m/s and takes 4.0 seconds to reach the ground. • a) What is the height from which the golf ball was projected? • b) What is the resultant velocity just before the object strikes the ground. • c) How far did the ball go?

26. YOU DO • Harry and Angela look from their balcony to a swimming pool below that is 15m from the bottom of their building. They estimate the balcony is 45m high and wonder how fast they would have to jump horizontally to succeed in reaching the pool. What do you think?