Vocabulary
Term
Free Fall
Definition
The acceleration of a falling object under the sole influence
of Earth’s gravitational force.
Free Fall Speed
The speed of a dropped object. The speed increases by 9.8
m/s every second.
Units: meters/second
Average Speed
Average of the initial and final speed of an object.
Terminal Speed
The maximum speed reached by an object in free fall; the
speed at which the forces of gravity and air resistance are
equal.
Air Resistance
The opposing force on a moving object due to friction of air.
Mass
The amount of matter an object has; a measure of an object’s
inertia; measured in kilograms.
Weight
A force created by gravity acting on mass.
Weight = mass x gravity
Or Fg = mg
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Section 2.3: Free Fall Speed
Definition
Formula
v = gt
Free Fall Speed
The speed of a dropped
object. The speed
increases by 9.8 m/s every
second.
V = velocity
g = gravity
9.8 m/s2
t = time
Key Ideas
When something falls through the air, the air
exerts an additional force. This force, called
air resistance, acts against the direction
of the object’s motion.
If you observe a falling object it stops
accelerating after a short distance and
falls at constant speed. An object only
accelerates until the force of air
resistance equals the force of gravity.
The net force then becomes zero and the
object falls with a constant speed called
the terminal speed.
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A rock dropped from the top of a cliff picks up speed as it falls. Pretend that a speedometer and
odometer are attached to the rock to show readings of speed and distance at 1-second intervals. Both
speed and distance are zero at time = zero (see sketch). Note that after falling 1 second the speed reading
is 10 m/sec and the distance fallen is 5 m. The readings for succeeding seconds of fall are not shown and
are left for you to complete. So record the position of the speedometer pointer and write in the correct
odometer reading for each time.
To simplify your calculations, you may use g = 10 m/sec2 and neglect air resistance.
Free Fall Speed
(m/s)
0
10
20
30
40
50
60
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Gravity is constantly pulling downward. If you throw a ball up, it will be decelerated by gravity. As the ball
moves upward, gravity will cause its speed to decrease by 9.8m/s each second. If an object is moving
downward, it will be accelerated by gravity. Its speed, v, will increase by 9.8 m/s each second.
The strength of the acceleration due to gravity is given the symbol, g, and it is equal to 9.8 m/s2.
Critical Thinking Questions
1. Of course, perfect “free fall” does not exist since there is always air resistance. But which of the
following objects behaves most similarly to an object in free fall?
a) confetti at a party b) a vase falling off a table c) a feather falling off a bird
2. The picture doesn’t show us what happens after 7 seconds. At a time of 8 seconds, how fast would the
ball be going?
(9.8 m/s2) x (8 s) to simplify these problems we will use gravity as 10 m/s2.
(10 m/s2) x (8 s) = 80 m/s
3. The ball in figure one started out at a speed of 29.4 m/s and took 3 seconds to reach its maximum
height. At a time of 3 seconds the speed of the ball was 0 m/s. If the beginning speed had been 39.2 m/s
(instead of 29.4 m/s), how many seconds would it have taken to reach a speed of 0 m/s?
4 s since it is slowing down at a rate of 9.8 meters/second every second.
4. If a rock fell off of a cliff, how fast would the rock be going after 2 seconds?
(10 m/s2) x (2 s) = 20 m/s
5. If a rock fell off a cliff, how fast would it be traveling after 8 seconds?
(10 m/s2) x (8 s) = 80 m/s
6. Which equation could be used to answer questions 4 and 5?
a) v = g · t
b) v = g + t
c) v = g · t2 + 2
d) v = 2( t + g )
7. If a ball is thrown upward at an initial velocity of 45.6 m/s, how many seconds will it take for the ball
to reach it’s maximum height? (Hint: use the equation from question 6; you know v and g, so you can
solve for t!)
Looking For
time
Given
g=10 m/s2
v=45.6 m/s
Relationship
v=gt
t=v/g
Solution
t=4.56 s
8. Considering the same ball from question 7, how long will it take for the ball to come back down for
you to catch it? (Hint: the ball will take the same amount of time to come down as it took to go up.)
4.56 s
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Information: Gravity and How Far A Rock Falls
The following information was gathered by scientists observing a rock falling down a cliff. The rock was
initially at rest with no speed and then began to fall:
Time (seconds)
Distance Fallen (meters)
0
0
1
4.9
2
19.6
3
44.1
4
78.4
Critical Thinking Questions
9. Which one of the following equations fits the data? (Note: d stands for distance fallen.)
a) d = g · t
b) d = 2(g · t)
c) d = ½ g · t2
d) d = t2 + 2g
10. A boy dropped a penny off a cliff. How many meters did the penny fall in 7 seconds?
d = ½ g · t2 = ½ (10 m/s2) (7 s)2 = 245 m
11. Considering the penny from the previous question, how fast was the penny going after 7 seconds?
(Hint: the equation from question 6 might help.
Looking For
Free fall speed
Given
g=10 m/s2
t=7 s
Relationship
v=gt
Solution
v=70 m/s
12. How long would it take a rock to fall down a cliff that is 109 m tall? (Hint: use the equation from
question 9 and solve for t.)
Looking For
time
Given
g=10 m/s2
d=109 m
Relationship
d=1/2 gt2
Solution
t=4.67 s
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Section 2.3: Average Speed
Definition
Formula
Vavg=(vf+vi)/2
Average Speed
Average of the initial and
final speed of an object.
Vf = final speed
vi = initial speed
t = time
Examples
1. A rock falls off a cliff and splashes into a river 5 seconds later.
What is the rock’s final speed (aka free fall speed)?
Looking For
Final speed
Given
g=10 m/s2
t=5 s
Relationship
v=gt
Solution
v=50 m/s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(50 m/s + 0)/2
=25 m/s
What was the rock’s average speed during its fall?
Looking For
Average speed
Given
Vi=0 m/s
Vf=50 m/s
t=5 s
2. A baseball is dropped from rest and falls for 2 seconds. What is the ball’s final speed (aka free fall
speed)?
Looking For
Final speed
Given
g=10 m/s2
t=2 s
Relationship
v=gt
Solution
v=20 m/s
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What is the average speed of a baseball dropped from rest that falls for 2 seconds?
Looking For
Average speed
Given
Vi=0 m/s
Vf=20 m/s
t=5 s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(20 m/s + 0)/2
=10 m/s
3. What is the final speed of a ball with an initial downward speed of 10 m/s that falls for 2 seconds?
Looking For
Final speed
Given
g=10 m/s2
t=2 s
Relationship
v=gt
Solution
v=20 m/s
What is the average speed of the ball if it has an initial speed of 10 m/s?
Looking For
Average speed
Given
Vi=10 m/s
Vf=20 m/s
t=2 s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(20 m/s +1 0)/2
=15 m/s
4. What is the final speed of a ball dropped from rest that falls for 8 seconds?
Looking For
Final speed
Given
g=10 m/s2
t=8 s
Relationship
v=gt
Solution
v=80 m/s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(80 m/s + 0)/2
=40 m/s
What is the average speed of the ball?
Looking For
Average speed
5.
Given
Vi=0 m/s
Vf=80 m/s
t=8 s
What is the final speed of an acorn that is dropped from rest by a squirrel and falls for 10 seconds?
Looking For
Final speed
Given
g=10 m/s2
t=10 s
Relationship
v=gt
Solution
v=100 m/s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(100 m/s + 0)/2
=50 m/s
Relationship
v=gt
Solution
v=70 m/s
What is the average speed of the acorn?
Looking For
Average speed
Given
Vi=0 m/s
Vf=100 m/s
t=10 s
6. What is the final speed of a ball that falls for 7 seconds?
Looking For
Final speed
Given
g=10 m/s2
t=7 s
What is the average speed of the ball if it is thrown with an initial speed of 5 m/s?
Looking For
Average speed
Given
Vi=5 m/s
Vf=70 m/s
t=7 s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(70 m/s + 5)/2
=37.5 m/s
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Free Fall Distance
d = distance
Formula
d = 4.9t2
Steps for Calculating
Formula
1. Calculate the
average speed.
2. Multiple the
average speed by
the time.
t = time
Examples
1. A skydiver falls for 6 seconds before opening her parachute.
a. Calculate the distance she has fallen in this time?
Looking For
Free fall distance
Given
t=6 s
Relationship
d=4.9t2
Solution
=4.9 x (62)
=176.4 m
2. An apple falls from the top branch of a tree and lands 1 second later. How tall is the tree? (calculate
free fall distance.)
Looking For
Free fall distance
Given
t=1 s
Relationship
d=4.9t2
Solution
=4.9 x (12)
=4.9 m
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Group Work
1. Peter drops a water balloon off the top of the school in an attempt to hit his nemesis Michael.
a. What is the ball’s free fall speed after 4 seconds in free fall?
Looking For
Free fall speed
Given
g=10 m/s2
t=4 s
Relationship
v=gt
Solution
v=40 m/s
b. What is the ball’s average speed after 4 seconds in free fall?
Looking For
Average speed
Given
Vi=0 m/s
Vf=40 m/s
t=4 s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(40 m/s + 0)/2
=20 m/s
c. What distance does the ball fall during the 4 seconds?
Looking For
Free fall distance
Given
t=4 s
Relationship
d=4.9t2
Solution
=4.9 x (42)
=78.4 m
2. During a science experiment, your teacher drops a toy doll “Ernesto” out of a window. Ernesto hits the
ground 3 seconds later.
a. What was Ernesto’s speed when he hit the ground after 3 seconds?
Looking For
Free fall speed
Given
g=10 m/s2
t=3 s
Relationship
v=gt
Solution
v=30 m/s
b. What was Ernesto’s average speed during the 3 seconds?
Looking For
Average speed
Given
Vi=0 m/s
Vf=30 m/s
t=3 s
Relationship
Vavg=(vf+vi)/2
Solution
Vavg=(30 m/s + 0)/2
=15 m/s
Given
t=3 s
Relationship
d=4.9t2
Solution
=4.9 x (32)
=44.1m
c. How high is the window?
Looking For
Free fall distance
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HomeWork
1. A penny is dropped into a wishing well. What was the free fall speed after 10 seconds?
Looking For
Free fall speed
Given
g=10 m/s2
t=3 s
Relationship
v=gt
Solution
v=30 m/s
2. In a bizarre but harmless accident, Superman fell from the top of the Eiffel Tower. How fast was
Superman traveling when he hit the ground 4.80 seconds after falling? (Hint: Calculate Superman’s
free fall speed after 4.80 seconds.)
Looking For
Final speed
Given
g=10 m/s2
t=4.80 s
Relationship
v=gt
Solution
v=48 m/s
3. A stone tumbles into a mine shaft and strikes bottom after falling for 4.2 seconds. How deep is the
mine shaft?
Looking For
Free fall distance
Given
t=4.2 s
Relationship
d=4.9t2
Solution
=4.9 x (4.22)
=86.436 m
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Weight
A force created by gravity
acting on mass.
Weight = mass x gravity
Or Fg = mg
Mass
The amount of matter an
object has; a measure of an
object’s inertia; measured in
kilograms.
Formula Formula
Fg = mg
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Examples
1. Calculate the weight of a 60-kg person on Earth.
Looking For
Weight
Given
m=60 kg
g=10 m/s2
Relationship
W=mg
Solution
(60 kg) x (10 m/s2)
=600 N
2. Calculate the weight of a 60-kg person on Mars where g=3.7 m/sec2.
Looking For
Weight
Given
m=60 kg
g=3.7 m/s2
Relationship
W=mg
Solution
(60 kg) x (3.7 m/s2)
=222 N
3. Legend has it that around 1587 Galileo dropped two balls from the Leaning Tower of Pisa to see which
would fall faster. Suppose the balls had masses of 1-kg and 10-kg.
a. Use the equation for weight to calculate the force of gravity on the 1-kg ball.
Looking For
Weight
Given
m=1 kg
g=10 m/s2
Relationship
W=mg
Solution
(1 kg) x (10 m/s2)
=10 N
b. Use the equation for weight to calculate the force of gravity on the 10-kg ball.
Looking For
Weight
Given
m=10 kg
g=10 m/s2
Relationship
W=mg
Solution
(10 kg) x (10 m/s2)
=100 N
Relationship
W=mg
Solution
(5 kg) x (10 m/s2)
=50 N
Relationship
W=mg
Solution
(45 kg) x (10 m/s2)
=450 N
Class Work
1. How much does a 5-kg backpack weigh on earth?
Looking For
Weight
Given
m=5 kg
g=10 m/s2
2. Jackie’s mass is 45-kg. What is her weight on Earth?
Looking For
Weight
Given
m=45 kg
g=10 m/s2
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