1. Agenda 1) Warm-Up 5 min 2) Vocab. Words 10 min 3) Projectile Motion Intro. 15 min 4) Pre-Lab Vectors 15 min 5) Vector Lab 30 min 11-08-11 Spring scale

2. Vocab. 1.Projectile: an object that moves through the air space, acted on only by gravity (and air resistance, if any) 2.Parabola: in projectile motion, it is the shape of the path traced by a projectile. 3.Trajectory: the curved path taken by a projectile. 4.Horizontal distance: the distance a projectile moves while falling; also called range. 5.Vertical component: vector which indicates the vertical velocity of a projectile; initial force. 6.Horizontal component: vector which indicates the horizontal velocity of a projectile; air resistance or inertial motion.

3. Projectile Motion: A projectile is any object that is projected by some means and continues in motion by its own inertia. Projectiles follow curved paths that have horizontal and vertical components of motion. Horizontal component of motion is completely independent of the vertical component of motion. Their combined effects produce the variety of curved paths that projectiles follows.

4. We find that projectiles move equal horizontal distances in equal time intervals since no acceleration takes place horizontally. The only acceleration is vertically in the direction of the earths gravity. The vertical component also changes and the horizontal component stays the same.

5. Move equal horizontal distances in equal time intervals.

6. The path traced by a projectile that accelerates only in the vertical direction while moving at constant horizontal velocity is called a parabola. When air resistance can be neglected, the curved paths are parabolic and the paths are called trajectories.

10. DUE TODAY: Projectile fill-in-blanks (KEEP) Vector Lab DUE NEXT CLASS: Finish Vector Lab questions & abstract Bring Calculator & Protractor! “Wisdom begins in wonder.” Socrates

13. Projectile Motion

14. Projectile – any object that is projected by some means and continues in motion by its own inertia EX: a cannonball shot from a cannon a stone thrown in the air a ball rolling off the table

15. Gravity acts DOWNWARD So, a ball moving horizontally has NO GRAVITY affecting its velocity. So, the only horizontal component is due to the initial force applied—NO acceleration is found in the horizontal axis.

16.  The horizontal direction is the x axis. Ignoring drag, there is no force acting on the projectile horizontally.  What keeps the object in MOTION is: Inertia which is present-1 st Law of Newton is being followed.  If the object slows down or stops—it is due to FRICTION.

17. If that ball is dropped, suddenly gravity acts on it to pull it down. Now it has a vertical component.

18.  g is constant in magnitude, always in the straight down direction, and always along the y axis; if air resistance is neglected; then, the motion of the center of mass is only due to the force of gravity accelerating or decelerating the mass.

19.  Projectile motion under the influence of near-Earth--- gravity will produce a curved path.  The vertical direction is on the “y “axis. The only force acting on any projectile vertically will be gravity. The acceleration will be the constant g = 9.806 65 m/s 2.

20.  KEY: What happens to a particle vertically does not affect its horizontal motion. The opposite is also true. The axes are independent.  NOTE what axis is CHANGING!!

22. Figure 6-15(Hewitt book) If a projectile had no gravity, it would move with this path:

23. Gravity pulls the projectile towards the Earth.

24. Those projectiles that accelerate only in a vertical direction while moving at a constant horizontal velocity have a path that forms a PARABOLA.

26. Air resistance is another force that acts on projectiles. It changes the path of a projectile like this:

27. IDEAL PATH ACTUAL PATH

28. If air resistance is negligible, a projectile will rise to its maximum height in the same amount of time it takes it to fall back down.

29. Without air resistance, the deceleration of the projectile going up is equal to the acceleration of the projectile coming back down.

30.  The range is the horizontal distance.  Solve for the time needed for the projectile to reach its maximum height (remember that gravity is acting) by using the “vertical” distance.  Once you know the time of flight, solve for the range by using: D H = Horizontal velocity X Time

31.  Satellite – an object that falls around Earth or some other body rather than falling into it because of its tremendous speed. ◦ Page 127 (Hewitt book)

32.  If no force acts horizontally, the motion found is at constant velocity- due to inertia.  The equation of motion is then D H = V H t.  BUT, to find V H when you have 2- dimensional motion, resolve the initial velocity into its horizontal component by using the formula : V H = V i cos 

33.  To find V v, resolve the initial velocity into its vertical component.  The formula to do this is: V v = V i sin Ø

34.  The time an object moves horizontally is the same as the time the object moves vertically.  So, Total time is the “time in the air” for a projectile at-an-angle.

35.  To find time: Remember that gravity is affecting the motion and therefore, the amount of time the projectile is in the air for “at an angle” will be TOTAL time.  So, t total = V v / g so D H = V H ( t t )

36. A vertical and a horizontal component. With the trajectory being the initial velocity*

38.  Acceleration is constant for a projectile.  Speed and velocity change at each point along the parabolic pathway.  What is the speed of the projectile at the very top of its pathway?  What is the acceleration of the projectile at the very top of its pathway?