Free FallCh. 2.5-2.9

Review• Average speed: what is it and how do we

figure it out?– average speed = distance/time

• Instantaneous speed?– the speed at any one instant

• Velocity?– Speed with direction

• Acceleration?– acceleration = velocity / time

Objectives

1. Describe free fall

2. Describe how air resistance affects the motion of falling objects

3. Explain why acceleration is a rate of a rate

Free Fall

• Drop an object

• Did this accelerate? At what rate?

• What does it mean to accelerate at 10m/s2 ?

• In every second, an objects speed increases 10m/s, or 10m/s2

Free Fall• Imagine that a speedometer

was strapped to a falling object . . .

• In every second, the objects speed increases by _____?

• What is the speedometer going to read (instantaneous speed) at each interval?

• Think about the relationship between velocity, acceleration, and time . . .

Free Fall• Would you rather catch a baseball dropped from 1m or off of a sky

scraper?• The speed of a falling object INCREASES over time.

Check Question• If a rock is dropped from the edge of a cliff, how

fast will it be going at the end of 1 second?• 10m/s• This object is experiencing free fall• Free fall:

– When object is only affected by gravity.

– No air resistance

• We call this “g”• g=10m/s2

Check Questions

• What will the speed of an object be that is dropped off of the edge of a cliff after 2 sec? 5 sec? (work it out and check your neighbor)

• 20m/s• 50m/s• What will it’s acceleration be after 15 seconds? (work

it out and check your neighbor)• 10m/s2

• g never changes!

• Is this ball accelerating?

• What was the relationship you wrote down earlier?

• Instantaneous speed= acceleration x elapsed time

• v = g t

• Is the object accelerating on it’s way up?

• Yes. How do you know?– b/c velocity is changing

• How much does it’s speed decrease each second?

• 10m/s2

• Acceleration during freefall is always 10m/s2, whether an object is thrown up or down!

Checkpoint• What is the objects

velocity at the top of the arch? (check neighbor)

• 0 m/s (for an instant)• What is the object’s

acceleration at the top of the arc? (check neighbor)– 10 m/s2 (acceleration

during freefall never changes!)

Free Fall: How Far• How FAST is an object falling after 1s? 2s? 10s?• 10m/s, 20m/s, 100m/s• How FAR has it fallen after 1 s?• 5m!• Anybody know why? Discuss with your neighbor• The object does not maintain a speed of 10 m/s

during that first second. It’s average speed is 5 m/s.• Use this formula:• Distance Fallen =(1/2)gt2

Practice

• You are bored and decide to drop your siblings favorite pet rock off of a cliff. How far will it far after 4 seconds? Work it out then check with neighbor.– Distance Fallen =(1/2)gt2

– (1/2)10 (4)2

– 5 (16)– 80 meters

• Distance Fallen =(1/2)gt2

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Try to catch the Try to catch the dollar bill!dollar bill!

• Try and catch the dollar bill!Try and catch the dollar bill!• Explanation: It takes at least 1/7 of a second Explanation: It takes at least 1/7 of a second

for nerve impulses to travel from the eye to the for nerve impulses to travel from the eye to the brain to the fingers. But according to the brain to the fingers. But according to the equation equation d =(1/2)gtd =(1/2)gt22, in only 1/8 of a second the , in only 1/8 of a second the bill falls 8 cm; half the length of the bill!!bill falls 8 cm; half the length of the bill!!

• D= 1/2(10)(.125)D= 1/2(10)(.125)22

= 0.078m, or 7.8cm= 0.078m, or 7.8cm

Hang Time• What is hang time?

– The amount of time a jumper is airborne.

• What do you think are some of the best hang times out there? Jordan? Spud Webb?

• Jordan’s is 0.98 sec• Spud’s is 1.2 sec• Both only about 1 second!

The Misconception

• A two second hangtime means 1 sec up and 1 sec down

• How far does an object fall in 1 sec?

• 5 meters or 16 ft! Wow, that’s quite a jump!!! Sorry, but it’s not happening.

Let’s Find Our Hang Time1. Stand facing a wall2. With feet flat on floor and arms extended upward,

make a mark (with tape) on the wall at the top of your reach. (use meters)

3. Move one step back from the first mark.4. Without taking more than ONE step into it, jump off

of BOTH feet. At the peak make another mark (with tape). Measure the distance in meters. (25cm = 0.25m)

5. The distance between those two jumps is your vertical leap.

- USE METERS! For example, 37 cm = 0.37m

6. Let’s figure out hang time…

Hang TimeLet’s do the math

• Force is applied when you leap upward• Greater the force --> greater the launch speed -->

higher the jump• As soon as your feet leave the ground, upward

speed immediately decreases at the rate of g, or 10m/s2

• At maximum height, your speed is 0.• You then fall at exactly the same rate, g.• Rising time = Falling time• Hang time is the sum of the rising and falling

times

Hang Time Continued . . .

• If we know the vertical height, we can plug it into this equation to get half of the actual hang time:

• d (your vertical leap) = distanceHang Time = the square root of (2d/g)

• Take this number and multiply it by 2.• That’s your hang time!• Another explanation

Air Resistance

• Feather vs. Penny• Air resistance noticeably alters the

motion of things like falling feathers and pieces of paper

• But, air resistance is less noticeable on more compact objects like a stone or baseball.

• We will learn more about this in ch. 5.

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Be patient…

• Be patient if it takes a few hours to achieve a clear understanding of motion. It took people nearly 2000 years from the time of Aristotle to Galileo to achieve as much!!