Transcript Projectile Motion

Class Presentation Outline
for
Projectile Motion
Created for CVCA Physics
By
Dick Heckathorn
28 November 2K+4
Needs updating from short one
Table of Contents
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28
31
A projectile is
Dropping an object
Laser Disk A: 41, 42, 43, 44
Dropping an Object
Throwing Horizontally
Dropping a Super Ball
Laser Disk B: 11, 12, 13, 14, 15
Problem: Thrown Horizontal
Problem: Horizontal Up
Problem: Horizontal Down p 205 # 45
Assumptions
A projectile is:
Any object that moves through
the air or through space acted
only on by gravity (and air
resistance if any).
We will ignore air resistance
unless information relative to it
is stated.
Dropping an object.
The only force acting on the
object is the pull of the earth
acting on it in a down direction.
This causes the object to
accelerate at the rate of 9.8 m/s2
in the same downward direction.
A 41 Free Fall Ride
Falling on Demon Drop
Accelerometer Shown
Always parallel to tracks
A 42, 43 Falling Bowling Ball
Bowling ball released from 4 m
A 44 Falling “Down Under” in
Australia
Object dropped in both
New York and Australia
Droping an object
To analyze the motion one uses
the five kinematic equations with
the variables: a, vi , vf , d and t.
Remember that you can use one
of the calculator programs to
find any two variables given the
other three.
Coffee Filter Investigation
Handout: #13 Air Resistance
Motion Sensor on Ceiling
Computer
Lab Pro
TI-83+
Printer – Online & Epson FX
Throwing an Object Horizontal
If one assumes that there is no
gravitational force of the earth on
the object…
it will travel in a horizontal
direction with a constant velocity.
Relative variables are: vh, dh, and t.
Throwing an Object Horizontal
It we deal with reality, there is the
force of gravity acting on the
object.
How does this force affect the
horizontal component of the
motion of the object?
Throwing an Object Horizontal
Demo: Super Ball
We can see that the force of
gravity acting on the ball does
not affect the horizontal motion
which is at right angles to the
direction of the force of gravity.
B 11 Projectile Motion
Ball was projected horizontally,
another dropped straight down
Later, horizontally lines drawn
Old PSSC – large white balls
B 12 Projectile Motion
Ball shot horizontally from
crossbow as a target ball is
dropped horizontally. Both
originally aligned horizontal.
Old PSSC – large white balls
B 13 Projectile Motion
Ball shot at an upward angle
from crossbow as a target ball is
dropped horizontally.
Old PSSC – large white balls
B 14 Projectile Motion
Ping pong balls glued to
plexiglas sheet at equal time
intervals
Old PSSC – Professor Hume
B 15a Projectile Motion
Air table is tilted so pucks
respond to “diluted gravity”.
One shot horizontal, one
dropped.
Frame 3573
B 15b Projectile Motion
Frame 3914
Determine range of angle
vs
angle of shot.
B 15c Projectile Motion
Frame 4385
Shot-putter
Throwing an Object Horizontal
We have seen that:
the horizontal and vertical
components do not affect each
other
the vertical motion is that of free
fall.
Throwing an Object Horizontal
Each component can be
analyzed independent of each
other.
We do so according to the
following:
Throwing an Object Horizontal
Horizontal
dh
vh
t
Vertical
a
vi
vf
dv
t
Problem 1
An object is thrown horizontally at 27
m/s from the edge of a cliff which is
40 m above the ground.
a. How long does it take to reach the
ground?
b. What is the range of the ball?
(Horizontal distance)
c. With what velocity did it strike the
ground?
How
reachand
theknow:
ground?
Welong
are to
given
Horizontal
dh = 77.2 m
vh = 27 m/s
t = 2.86 s
Vertical
a = 9.8 m/s2 ↓
vi = 0 m/s
vf = 28 m/s ↓
dv = 40 m ↓
t = 2.86 s
The
velocity
value
vf it
Solve
for ‘t’
?is: ?
dfor
:as
?
h by:
strikes the ground: ?
38.9 m/s
H 46.0o D
Problem 2
An object is thrown with a speed of
725 m/s at an angle of H 60o U.
a. How long does it take to reach the
ground?
b. What is the range of the ball?
(Horizontal distance)
c. With what velocity did it strike the
ground?
First find the horizontal and
vertical component of the initial
velocity.
730 m/s
632 m/s
60o
365 m/s
We are given and know:
Horizontal
dh = 47085 m
vh = 365 m/s
t = 129
64.5ss no
Vertical
2
9.8
m/s
↓
a =
vi = 632 m/s ↑
m/s
0 m/s
vf = 632
no↓
dv = 20379 m ↑
t = 64.5 s
value
d?v?itis: ? 730 m/s
Solve
for tdfor
by:
The
velocity
as
h is:
strikes the ground: ? H 60.0o D
OR
Horizontal
dh = 47085 m
vh = 365 m/s
t = 129 s
Vertical
2
9.8
m/s
↓
a =
vi = 632 m/s ↑
vf = 632 m/s ↓
dv = 20379 m ↑
t = 129 s
value
d?v?itis: ? 730 m/s
Solve
for tdfor
by:
The
velocity
as
h is:
strikes the ground: ? H 60.0o D
Problem 3
A bomber, diving at an angle of
53o with the vertical, releases a
bomb at an altitude of 730 m. The
bomb hits the ground 5.0 sec
after being released.
Problem 3
First find the horizontal and
vertical component velocities of
the bomb.
161.2 m/s
121.5 m/s 53o
202 m/s
We are given and know:
Horizontal
dh = 806 m
vh = 161.2 m/s
t = 5.0 s
Vertical
2
9.8
m/s
↓
a =
vi = 121.5 m/s ↓
vf = 170.5 m/s↓
dv = 730 m ↓
t = 5.0 s
velocity
it
The value
foras
v
is:
t fhis:
d
is:??? ___ m/s
strikes the ground: ? H ____ D
Assumptions Projectile Motion
1. The effect air resistance has
been ignored.
Air resistance will shorten the
horizontal distance a ball will
go.
A baseball projected to go
120-m will only go 71.4-m.
Assumptions Projectile Motion
2. The acceleration due to gravity
is constant.
We will find that the acceleration
due to gravity varies inversely
proportional to the square of the
distance from the center of the
earth.
Assumptions Projectile Motion
3. The earth is assumed to be flat
as the circumference is very
large.
Thus for large horizontal
distances the calculated
distance is not exactly correct.
Assumptions Projectile Motion
4. Projectile remains in same
vertical plane during flight.
A projectile launched directly
north will not follow the
longitudinal line from which it
is launched due to the rotation
of the earth on its axis.
Need for a computer
When sending a rocket to the
moon, constant calculations are
needed to update the corrections
need to get the rocket to the
moon.
When the computers went down
on Apollo 13, there was nothing
to update the data.
Apollo 13 Video
Scene when aligning up
spacecraft to enter earth’s
atmosphere at the correct angle.
Article
Notes from the Military
That’s all folks!