Unit 3: Projectile & 2D Motion

1. Unit 3: Projectile & 2D Motion http://www.youtube.com/watch?v=sFcsMDzW1Yg

2. 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.

3. 2 Dimensional Motion • Projectiles • Gravity affects outcome • Riverboats & Airplanes • Gravity does not affect outcome

5. If a cannonball is projected horizontally from the top of a cliff. In the absence of gravity, the cannonball would continue its horizontal motion at a constant velocity. • Horizontal velocity is constant (ax = 0) • If dropped from rest in the presence of gravity, the cannonball would accelerate downward. • Vertical velocity gains speed (ay = -9.8 m/s2)

6. Monkey In the Absence of Gravity

7. Why Does the Hunter Miss the Monkey?

8. The Hunter Now Aims

9. Strategies for Applying Kinematic Equations in 2 Dimensions • Make a drawing of the situation. • Decide which directions to be called positive and negative. Do this for both the x and y directions. • Remember that the time variable is the same for both x and y. • Make note of all the assumed information. • Starts at rest. • Stops • When motion is divided into two segments, remember the final velocity for one segment becomes the initial velocity for the next segment. • Make notice of the situation…do you multiply or divide the time by 2… or leave it?

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

11. 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 Launch velocity Launch angle Ending velocity

12. 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!

13. EX 1: A football is kicked at an angle of 45º to the ground with a speed of 25 m/s. Calculate … • A. The initial horizontal velocity • B. The initial vertical velocity • C. Maximum height reached

14. EX 2: 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

15. 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. -Use second half of trajectory. -Plugging in values:

16. 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 (Vx and Vy). Vx is found using: Vy is found using half of trajectory and: Knowing that Vy is zero at half the time … So …

17. A launched projectile has a horizontal displacement of 53 meters and total time 7 seconds. Calculate … • C. Launch Angle. θ

18. Ex 3: An object is launched horizontally from a height of 350 meters and lands 900 meters horizontally. Calculate … • Velocity of object.

19. Ex 4 An object is travelling at 37◦from vertical at velocity 8 m/s. How long will it take to go 38 m horizontally? • NOT A PROJECTILE!!!! • Need X component velocity. Note that (similar to projectiles) time is shared between two motions. Each component is independent of the other. θ=37

20. 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?