Free Fall
Free fall – motion under
the influence of the
gravitational force only
(neglects air resistance)
1
Elapsed time
time that has passed
from the beginning of
a fall
2
Gravity and Free fall
Acceleration due to gravity
is 9.8 m/s2
, downward
Every second that an
object falls, the velocity
i...
Sample 1
If an object is dropped from rest at the
top of a cliff, how fast will it be going
after 1 second?
2 seconds?
10 ...
First, Identify the GIVENS?
When an object is falling, assume that
a = 9.8 m/s2
“from rest” tells us that Vi = 0
“how fast...
Therefore…
G: a = 9.8 m/s2
Vi = 0
t = 1 s
U: Vf = ?
E: Vf = Vi + at
S: Vf = 0 + (9.8 m/s2)
(1 s)
S: Vf = 9.8 m/s
6
Now find out how fast it will be
falling after 2 s…
G: a = 9.8 m/s2
Vi = 0
t = 2 s
U: Vf = ?
E: Vf = Vi + at
S: Vf = 0 + (...
Now find out how fast it will be
falling after 10 s…
G: a = 9.8 m/s2
Vi = 0
t = 10 s
U: Vf = ?
E: Vf = Vi + at
S: Vf = 0 +...
Calculating How Fast Free
Fall Is
If we use Vf = Vi + at, and Vi = 0 then we actually
have an equation that reads… Vf = at...
Sample Problem #2
The Demon Drop ride at Cedar
Point Amusement Park falls
freely for 1.5 s after starting
from rest.
What ...
What is its velocity at the end
of 1.5 s?
G: a = 9.8 m/s2
Vi = 0 (starting from rest)
t = 1.5 s
U: Vf = ?
E: Vf = Vi + at
...
How far does it fall?
G: a = 9.8 m/s2
Vi = 0
t = 1.5 s
Vf = 14.7 m/s (from previous part)
U: d = ? (how far)
E: d = Vit + ...
Calculating How Far Free
Fall Is
If we use d = Vit + ½ at2
, and Vi = 0 then we
actually have an equation that reads…
d = ...
Acceleration due to Gravity
If the object is moving down, a = 9.8 m/s2
If the object is moving up, a = - 9.8 m/s2
a = 9.8 ...
Throwing an object into the air
When an object is thrown into the air, the
velocity at its highest point is ZERO!!!
Begin
...
Sample Problem #3
A ball is thrown vertically into the air with an
initial velocity of 4 m/s.
How high does the ball rise?...
How high does the ball rise?
HINT: draw a picture and label it
Begin
Vi = 4 m/s
End
Vf = 0 m/s
d= ?
17
How high does the ball rise?
G: a = -9.8 m/s2
(notice the negative sign, ball moving upward)
Vi = 4 m/s
Vf = 0 m/s (at the...
How long does it take to reach its
highest point?
G: a = -9.8 m/s2
U: t = ?
Vi = 4 m/s
Vf = 0 m/s
d = 0.816 m
E: Vf = Vi +...
If the ball is caught in the same spot
from which it was thrown, what is
the total amount of time that it was
in the air?
...
G: a = 9.8 m/s2
(ball moving down before it is caught)
Vi = 0 m/s
d = 0.816 m
t = 0.408 s
U: Vf = ?
E: 2ad = Vf
2
– Vi
2
,...
You’re done!
Now try some
problems on your
own.
22
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Free fall

  1. 1. Free Fall Free fall – motion under the influence of the gravitational force only (neglects air resistance) 1
  2. 2. Elapsed time time that has passed from the beginning of a fall 2
  3. 3. Gravity and Free fall Acceleration due to gravity is 9.8 m/s2 , downward Every second that an object falls, the velocity increases by 9.8 m/s 3
  4. 4. Sample 1 If an object is dropped from rest at the top of a cliff, how fast will it be going after 1 second? 2 seconds? 10 seconds? 4
  5. 5. First, Identify the GIVENS? When an object is falling, assume that a = 9.8 m/s2 “from rest” tells us that Vi = 0 “how fast will it be going?” is asking us to find Vf = ? (this is the unknown) the first problem gives us a time of t = 1 s Work this on YOUR paper using GUESS… 5
  6. 6. Therefore… G: a = 9.8 m/s2 Vi = 0 t = 1 s U: Vf = ? E: Vf = Vi + at S: Vf = 0 + (9.8 m/s2) (1 s) S: Vf = 9.8 m/s 6
  7. 7. Now find out how fast it will be falling after 2 s… G: a = 9.8 m/s2 Vi = 0 t = 2 s U: Vf = ? E: Vf = Vi + at S: Vf = 0 + (9.8 m/s2) (2 s) S: Vf = 19.6 m/s 7
  8. 8. Now find out how fast it will be falling after 10 s… G: a = 9.8 m/s2 Vi = 0 t = 10 s U: Vf = ? E: Vf = Vi + at S: Vf = 0 + (9.8 m/s2) (10 s) S: Vf = 98 m/s 8
  9. 9. Calculating How Fast Free Fall Is If we use Vf = Vi + at, and Vi = 0 then we actually have an equation that reads… Vf = at, where a = 9.8 m/s2 . When a = 9.8 m/s2 , we call that constant g. Therefore, we can use the following new, or derived equation… Instantaneous speed = acceleration X elapsed time v = gt 9
  10. 10. Sample Problem #2 The Demon Drop ride at Cedar Point Amusement Park falls freely for 1.5 s after starting from rest. What is its velocity at the end of 1.5 s? How far does it fall? 10
  11. 11. What is its velocity at the end of 1.5 s? G: a = 9.8 m/s2 Vi = 0 (starting from rest) t = 1.5 s U: Vf = ? E: Vf = Vi + at S: Vf = 0 + (9.8 m/s2) (1.5 s) S: Vf = 14.7 m/s 11
  12. 12. How far does it fall? G: a = 9.8 m/s2 Vi = 0 t = 1.5 s Vf = 14.7 m/s (from previous part) U: d = ? (how far) E: d = Vit + ½ at2 (use any of the 3 motion formulas with d in them) S: d = (0)(1.5s) + ½ (9.8 m/s2 )(1.5s)2 S: d = 11.03 m 12
  13. 13. Calculating How Far Free Fall Is If we use d = Vit + ½ at2 , and Vi = 0 then we actually have an equation that reads… d = ½ at2 , where a = 9.8 m/s2 . When a = 9.8 m/s2 , we call that constant g. Therefore, we can use the following new, or derived equation… d = ½ gt2 13
  14. 14. Acceleration due to Gravity If the object is moving down, a = 9.8 m/s2 If the object is moving up, a = - 9.8 m/s2 a = 9.8 m/s2 (speeding up) a = - 9.8 m/s2 (slowing down) 14
  15. 15. Throwing an object into the air When an object is thrown into the air, the velocity at its highest point is ZERO!!! Begin Vi = ? Begin Vi = 0 m/s End Vf = 0 m/s End Vf = ? 15
  16. 16. Sample Problem #3 A ball is thrown vertically into the air with an initial velocity of 4 m/s. How high does the ball rise? How long does it take to reach its highest point? If the ball is caught in the same spot from which it was thrown, what is the total amount of time that it was in the air? What is its velocity just before it is caught? 16
  17. 17. How high does the ball rise? HINT: draw a picture and label it Begin Vi = 4 m/s End Vf = 0 m/s d= ? 17
  18. 18. How high does the ball rise? G: a = -9.8 m/s2 (notice the negative sign, ball moving upward) Vi = 4 m/s Vf = 0 m/s (at the top, before it starts to fall, it stops) U: d = ? E: 2ad = Vf 2 – Vi 2 , (solve for d) d = Vf 2 – Vi 2 2a S: d = 02 – (4 m/s)2 2(-9.8 m/s2 ) S: d = 0.816 m 18
  19. 19. How long does it take to reach its highest point? G: a = -9.8 m/s2 U: t = ? Vi = 4 m/s Vf = 0 m/s d = 0.816 m E: Vf = Vi + at, (solve for t) t = Vf – Vi a S: t = 0 m/s – 4 m/s (-9.8 m/s2 ) 19
  20. 20. If the ball is caught in the same spot from which it was thrown, what is the total amount of time that it was in the air? G: a = 9.8 m/s2 (ball going down, positive) U: t = ? Vi = 4 m/s Vf = 0 m/s d = 0.816 m E: d = Vit + ½ at2 ; derived to d = ½ gt2 , solve for t… t2 = (2d)/g S: t2 = (2)(0.816 m)/(9.8 m/s2 ) *don’t forget to take the square root S: t = 0.408s Total time = time Going up + time going down Total time = 0.408s +0.408s = 0.816s 20
  21. 21. G: a = 9.8 m/s2 (ball moving down before it is caught) Vi = 0 m/s d = 0.816 m t = 0.408 s U: Vf = ? E: 2ad = Vf 2 – Vi 2 , (solve for Vf) Vf 2 = 2ad + Vi 2 S: Vf 2 = 2(9.8 m/s2 )(0.816 m) + 02 S: Vf = 3.99 or 4 m/s What is its velocity just before it is caught? 21
  22. 22. You’re done! Now try some problems on your own. 22
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