2. Page 1 Freefall

3. Page 2 Freefall What is freefall? Which of the following things do you think are in freefall? Drop a ball from rest Toss it upward Throw it downward Throw it in an arc to a student Bounce a ball Launch it from slingshot Freefall means that no other forces other than the object’s weight are acting on the object

4. Page 3 Free fall http://nssdc.gsfc.nasa.gov/planetary/lunar/apollo_ 15_feather_drop.html At the end of the last Apollo 15 moon walk, Commander David Scott performed a live demonstration for the television cameras. He held out a geologic hammer and a feather and dropped them at the same time. Because they were essentially in a vacuum, there was no air resistance and the feather fell at the same rate as the hammer, as Galileo had concluded hundreds of years before - all objects released together fall at the same rate regardless of mass

5. Page 4 Acceleration due to gravity Technically, the acceleration is 9.8 m/s 2, but we will always use 10 m/s 2 toward the ground

6. Page 5 Consider a coin flipped into the air and returning to the hand..... The up and down trip is absolutely symmetrical. The coin spends half of the time rising and half falling. The speed when the coin returns to the hand equals the speed with which the coin left the hand. The coin undergoes an acceleration of 10 m/s 2 during both halves of the trip. Symmetry in free fall

7. Page 6 Steps We will use the same 3 equations we have been, the motion will just be vertical now and the acceleration will not be explicitly stated. Air resistance will always be ignored.

8. Page 7 Example A stone is dropped at rest from the top of a cliff. It is observed to hit the ground 5.78 s later. How high is the cliff? What do I know? What do I want? v oy = 0 m/sΔy = ? a = -10 m/s 2 y o = 0 m t = 5.78 s Which variable is NOT given and NOT asked for? Final Velocity! -167.0 m h =167.0m

9. Page 8 Example You drop a ball from a 120 m high cliff. a) How long is the ball in the air? b) What is the ball's speed and velocity at impact? c) What is the velocity when the ball has fallen half way down? d) How long does it take to reach the half way point?

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11. Page 10 Example You throw a ball straight up into the air. It leaves your hand with a velocity of 20 m/s, and you catch it a moment later. a) How long is the ball in the air? b) How high above your hand will the ball rise? c) What is the velocity of the ball when you catch it? d) What is the acceleration of the ball at its highest point?

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13. Page 12 Example A helicopter is ascending vertically with a speed of 5.00 m/s. At a height of 105 m above the ground, a package is dropped from the window. How long does it take for the package to hit the ground?

14. Page 13 Example Old Faithful, that geyser thing erupts regularly shooting a stream of smoking hot water to an average height of 396 m (for real). (a) With what velocity does the water leave the ground? (b) How long does it take for the water stream to reach its maximum height? (c) What is the velocity of the water stream at 13 seconds?

15. Page 14 Relationships Let’s use the kinematics equations to answer these: 1. A mango is dropped from a height h. a. If dropped from a height of 2 h, would the impact speed double? b.Would the air time double when dropped from a height of 2 h ?

16. Page 15 2.A mango is thrown down at a speed v. a.If thrown down at 2 v from the same height, would the impact speed double? b.Would the air time double in this case?

17. Page 16 Relationships (cont.) 3.A rubber chicken is launched straight up at speed v from ground level. Find each of the following if the launch speed is tripled (in terms of any constants and v). a.max height b.hang time c.impact speed 3 v3 v 9 v 2 / 2 a 6 v / a Answers