Dive Safety Dive Safety You are part of a citizen's group evaluating the safety of a You are part of a citizen's group evaluating the safety of a high school athletic program. To help judge the diving high school athletic program. To help judge the diving program you would like to know how fast a diver hits the program you would like to know how fast a diver hits the water in the most complicated dive. The coach has his best water in the most complicated dive. The coach has his best diver perform for your group. The diver, after jumping from diver perform for your group. The diver, after jumping from the high board, moves through the air with a constant the high board, moves through the air with a constant acceleration of 9.8 m/sacceleration of 9.8 m/s22. Later in the dive, he passes near a . Later in the dive, he passes near a lower diving board which is 3.0 m above the water. With lower diving board which is 3.0 m above the water. With your trusty stop watch, you determine that it took 0.20 your trusty stop watch, you determine that it took 0.20 seconds to enter the water from the time the diver passed seconds to enter the water from the time the diver passed the lower board. How fast was he going when he hit the the lower board. How fast was he going when he hit the water? water?

Lesson #12Lesson #12Topic: Topic: Gravitational AccelerationObjectives: Objectives: (After this class I will be able to)(After this class I will be able to)

1. Describe the difference between falling objects and regularly accelerating objects.

2. Explain what factors affect the acceleration of a falling object.

9/19/07

Assignments: Section 3-2 & 3-3 quizzes due tomorrow “Vertical Acceleration” due Friday Acceleration Quiz on Friday

Project: Toss a ball in the air and describe its acceleration. (How does velocity change over time?)

Acceleration due to Gravity:Acceleration due to Gravity:

All objects will fall towards the center of the All objects will fall towards the center of the earth with a constant acceleration.earth with a constant acceleration.

The rate in which they accelerate is The rate in which they accelerate is completely completely independentindependent of size, shape, of size, shape, height, mass, or initial velocity (despite height, mass, or initial velocity (despite direction)direction)

This constant rate is called g.This constant rate is called g.

g=-10m/sg=-10m/s22

g g never never equals zero. equals zero.

The acceleration of a falling object The acceleration of a falling object depends on…depends on…

Its

mas

s

Its

size

Its

initi

al v

eloci

ty

Its

initi

al h

eigh

t

The

mas

s of

the

Earth

..

0% 0% 0%0%0%

1.1. Its massIts mass

2.2. Its sizeIts size

3.3. Its initial velocityIts initial velocity

4.4. Its initial heightIts initial height

5.5. The mass of the The mass of the Earth.. Duh! Earth.. Duh!

0 of 20

Positive and Negative DirectionPositive and Negative DirectionVectorVector: magnitude with direction: magnitude with direction

Ex. Displacement, Velocity, AccelerationEx. Displacement, Velocity, Acceleration

Direction is represented with positive and Direction is represented with positive and negative values.negative values.

Upward direction is positiveUpward direction is positive

Downward direction is negativeDownward direction is negative

Example: (write all givens)

A ball is tossed 3.2 meters into the air with an initial velocity of 8m/s.

Positive and Negative DirectionPositive and Negative DirectionExample: (write all givens)

A boy throws a water balloon out of a tree house towards the ground with a velocity of 3m/s and hits the person standing 6m below him.

Problem Solving with gravityProblem Solving with gravityWe can still use all of our kinematics equations for falling objects.

Except now a = ga = g

vf = vi + gt d= vit + ½ gt2 vf2 = vi

2 + 2gd

A ball is thrown upward. On the way up it is A ball is thrown upward. On the way up it is accelerating _______. On the way down it is accelerating _______. On the way down it is

accelerating ________.accelerating ________.

Upwar

d, upw

ard

Upwar

d, dow

nward

Downwar

d, d

ownward

Downwar

d, u

pward

0% 0%0%0%

1.1. Upward, upwardUpward, upward

2.2. Upward, downwardUpward, downward

3.3. Downward, downwardDownward, downward

4.4. Downward, upwardDownward, upward

0of20

What is the acceleration of a ball What is the acceleration of a ball tossed straight into the air with an tossed straight into the air with an

initial velocity of 15m/s?initial velocity of 15m/s?

15

m/s

2

7.5

m/s

2

-10

m/s

2

10

m/s

2

0% 0%0%0%

1.1. 15 m/s15 m/s22

2.2. 7.5 m/s7.5 m/s22

3.3. -10 m/s-10 m/s22

4.4. 10 m/s10 m/s22

0

0

20

ProjectProject

Reaction Time: Reaction Time:

Pick a partner and drop a ruler through their Pick a partner and drop a ruler through their hand with their fingertips even with the hand with their fingertips even with the 0cm mark. Then use the distance that the 0cm mark. Then use the distance that the ruler fell to determine their reaction time.ruler fell to determine their reaction time.

Remember: Write down your unknown, Remember: Write down your unknown, givens, original equation, and algebra givens, original equation, and algebra before solving. before solving.

Practice ProblemsPractice Problems

1. A geyser in Yellowstone national park is capable of shooting hot water up from the ground with a speed of 48m/s. How high can this geyser shoot?

Practice ProblemsPractice Problems

2. A bird in its nest has a worm in its mouth and while trying to drop the worm to its baby, it misses and the worm drops to the ground in 1.5 seconds. How high is the nest?

Practice ProblemsPractice Problems3. Why is it a sure bet that a 15.5 cm dollar bill cannot be

caught by your friend if his reaction time is 0.2 seconds and the bill is dropped when the bottom edge of the bill is even with the tips of his fingers?

Critical Thinking ProblemCritical Thinking ProblemA ball is tossed straight upward into the air. It reaches a A ball is tossed straight upward into the air. It reaches a

maximum height of 45m before falling back down.maximum height of 45m before falling back down.How long was the ball in the air?How long was the ball in the air?

What was its velocity when it left the person’s hand?What was its velocity when it left the person’s hand?

What was its velocity when it fell back into the person’s What was its velocity when it fell back into the person’s hand?hand?

Create a velocity vs. time graph of the ball’s motion.Create a velocity vs. time graph of the ball’s motion.

Critical Thinking ProblemCritical Thinking Problem30m/s

20m/s

10m/s

-30m/s

-20m/s

-10m/s

0m/s

1s 2s 3s 4s 5s 6s

Free fall accelerationFree fall acceleration

Assignment: Assignment:

p85 Standardize Test Practice #1 – 7p85 Standardize Test Practice #1 – 7

Get to the chopper quizGet to the chopper quiz

A baseball is thrown vertically into A baseball is thrown vertically into the air with an initial speed of the air with an initial speed of

30m/s. After 2 seconds the ball’s 30m/s. After 2 seconds the ball’s acceleration is…acceleration is…

15m

/s

15m

/s2

-15m

/s2

10m

/s2

-10m

/s2

0%

9%

55%

18%18%

1.1. 15m/s15m/s

2.2. 15m/s15m/s22

3.3. -15m/s-15m/s22

4.4. 10m/s10m/s22

5.5. -10m/s-10m/s22

A race car starts from rest. 5 A race car starts from rest. 5 seconds later it has achieved a seconds later it has achieved a

velocity of 25m/s. The acceleration velocity of 25m/s. The acceleration of the car is…of the car is…

0m

/s2

5m

/s

5m

/s2

-10m

/s2

10m

/s2

-10m

/s

0% 0%

9%

0%0%

91%1.1. 0m/s0m/s22

2.2. 5m/s5m/s

3.3. 5m/s5m/s22

4.4. -10m/s-10m/s22

5.5. 10m/s10m/s22

6.6. -10m/s-10m/s

Critical Thinking ProblemsCritical Thinking ProblemsA bullet is fired vertically into the air. It remains in the air for A bullet is fired vertically into the air. It remains in the air for

12 seconds before falling back to the ground. 12 seconds before falling back to the ground. How high did the bullet go into the air?How high did the bullet go into the air?

With what velocity did it leave the gun?With what velocity did it leave the gun?

With what velocity did it return to ground?With what velocity did it return to ground?

Create a velocity vs. time graph of the bullet’s motionCreate a velocity vs. time graph of the bullet’s motion

Critical Thinking ProblemCritical Thinking Problem60m/s

40m/s

20m/s

-60m/s

-40m/s

-20m/s

0m/s

2s 4s 6s 8s 10s 12s

Old Stuff Bonus (2pts)Old Stuff Bonus (2pts)Two trains are traveling towards one another and Two trains are traveling towards one another and

each train is traveling at 10km/h. When the each train is traveling at 10km/h. When the trains are 20 km apart, a bee begins flying from trains are 20 km apart, a bee begins flying from one train to the other at a steady speed of one train to the other at a steady speed of 30km/h. When it gets to the one train it quickly 30km/h. When it gets to the one train it quickly turns around and flies back to the other train. It turns around and flies back to the other train. It keeps doing this over and over until the trains keeps doing this over and over until the trains meet and SQUISH! meet and SQUISH!

How many kilometers did the bee travel in its total How many kilometers did the bee travel in its total back-and-forth trips?back-and-forth trips?