a = Velocity final – Velocity initial time

1. a = Velocityfinal – Velocityinitialtime • Solve for Velocityfinal with algebra • A new (but old) formula Velocityfinal= Velocityinitial+ at

2. Velocityfinal= Velocityinitial+ at • Calculate the instantaneous speed at the 10 s mark for a car that accelerates at 2 m/s² from a position at rest • Velocityfinal= Velocityinitial+ at = 0 m/s +2 m/s² (10 s) = 20 m/s

3. Free Fall • Definition- when an object is moving solely (only) under the influence of gravity….

4. Example of gravity • Dropping a ball? • Throwing a ball? • Yes • Yes, once it leaves your hand

5. Experience tells you that objects speed up (or accelerate) as they fall • All objects always accelerate at the same rate • (when we ignore air resistance)

6. Ignoring air resistance

7. On the moon • http://www.youtube.com/watch?v=U7db6ZeLR5s

8. So what is that magical number that all objects accelerate at? 9.8 m/s²

9. Finish the definition of free fall • Definition- when an object is moving solely (only) under the influence of gravity…. • (when we ignore air resistance)

10. The History of the Law of Falling Bodies Galileo Galilei (1564-1642)

11. Galileo is said to have dropped two unequal weights from the top of the Leaning Tower of Pisa to prove his theory. Galileo claimed that a naturally falling object would gain equal amounts of velocity in equal amounts of time. If correct, this means that i) the object’s speed increases as it falls and ii) the rate at which it picks up speed does not change during the fall.

12. However, for medieval science, freely falling objects moved too quickly and the clocks could not record quickly enough . So Galileo devised to slow down the motion by replacing the falling object with a ball rolling down a gently inclined plane.

13. The velocity of a free-falling object which has been dropped from a position of rest is dependent upon the time for which it has fallen. Time (s) Velocity (m/s) 0 0 1 9.8 2 19.6 3 29.4 4 39.2 5 49.0

14. Gravity • Causes free falling objects to accelerate at 9.8 m/s² toward the center of the earth. • The symbol is g (for acceleration due to gravity)

15. Gravity • Positive or negative?...that’s the question! • By convention…. • + 9.8 when an object is falling towards the earth - 9.8 when an object is moving away from the earth

16. How fast something is moving is very different from how far • How far does an object fall in 1 s? • It is 4.9 m….why? • In free fall, the object started from rest and is not at a constant speed Velocityavg=Vfinal + Vinitial 2

17. How far will an object drop? • d= ½ gt² • I drop a rock off of a bridge, and 4.2 s later, I hear a splash. What is the height of the bridge? • d= ½ (9.8 m/s²) (4.2 s)² = 86 m

18. Kinematics Formula Summary • vf = vi + gt • d = vit + ½½gt2 if velocity is 0 then the equation • vf2 = vi2 + 2gd

19. Practice Problem You drop a ball from rest off a 120 m high cliff. Assuming air resistance is negligible (free fall), how long is the ball in the air? What is the ball’s speed when it strikes the ground at the base of the cliff?

20. Answer • t = 4.95s • vf =48.5m/s

21. Review • http://onlinephys.com/freefall6.gif • http://onlinephys.com/freefall5.gif

22. What’s the story?

23. Free Fall with Upward Motion • When something is thrown straight upward under the influence of gravity, and then returns to the thrower, this is very symmetrical = parabola • The object spends half its time traveling up; half traveling down.

24. Free Fall with Upward Motion • Velocity when it returns to the ground is the opposite of the velocity it was thrown upward with. • Acceleration is 9.8 m/s2 and directed DOWN the entire time the object is in the air!

25. Free Fall with Upward Motion

26. Free Fall with Upward Motion • Homer Hickham used this fact to determine how high his rocket went  and that the rocket boys didn’t start the fire in Welch

27. October Sky • http://www.youtube.com/watch?v=udHB3tftPz4