Projectile Motion

1
Projectile Motion

• Materials
• Two different balls.
• Sheet of butcher paper.
• Markers.
• Procedures (with your lab group)
• Each group needs two DIFFERENT balls and a sheet
  of butcher paper.
• Fold your butcher paper to make two different
  sections.
• Spend a few minutes throwing your balls between
  partners to determine what the flight path looks
  like. Be sure to observe the flight path from at
  least two different reference points.
• Sketch the flight path of your balls on the
  paper.
• Determine what factors affect the shape and
  duration of the flight.
• List factors on your sheet.
• Be prepared to present to the class.

2
History of Inertia

• A tale of projection

3
Aristotle 384-322 BC
Proposed that everything must have a continuous
motive force in order to keep an object in
motion. Also believed that the natural place
for an object is resting on the ground, and any
force which opposes this position is known as a
violent force and is eventually overcome.
4
Suggested the motion of an arrow was such,
because air rushes from the front to fill the
possible vacuum at the rear this then causes
turbulence which pushes on the arrow to keep it
in motion. But also the air resists this forward
motion and eventually slows down the arrow. The
natural force then is able to take over and
return the arrow to its natural position on the
ground. Ignored celestial motion because this
motion was also seen as natural.
5
John Philoponus600 AD
Impressed force

• About 500AD he challenged Aristotles beliefs
  about motion (To be fair, Aristotle also had
  doubts.)
• Suggested an impressed force kept the arrow in
  motion, but any impressed force eventually dies
  out, even in a void
• The idea that motion can go on forever did not
  occur to him.

6
Jean Buridan 1300 AD
Impetus

• Proposed that the arrow is given an impetus by
  the bow an impetus was not expected to die out
  if it were not expended in overcoming air
  resistance.
• His thinking marks an important shift from
  external agents propelling the object to some
  acquired internal property or state.

7
Galileo 1564-1642

• Defended the Copernican belief that the earth
  rotates. Some said that if the earth rotates, an
  arrow shot directly upward would then land some
  distance to the west. For there was nothing to
  keep it moving horizontally with the spin of the
  earth.
• Did experiments with pendulums and in inclined
  planes which helped him to come up with, A body
  will continue to move with constant speed on a
  frictionless infinite horizontal plane.
• Also continued to ignore celestial motion because
  he thought it was natural and needed no
  explanation

8
René Descartes 1596-1650

• Extended the idea of inertia to all bodies
  including celestial bodies.
• Pointed out circular motion is constrained motion
  (always pulling inward) Therefore celestial
  bodies motion must be explained is not natural
  motion
• A vertical fall does not happen at a constant
  speed and therefore must be caused by some
  external influence.
• He did not go beyond his statements about inertia
  so most of the credit goes to Sir Isaac Newton,
  who used them to build a foundation for mechanics.

9
Galileos Experiments
10
Galileos Thought Experiment

• Prior to the 16th century the path of a
  projectile was assumed to consist of an initial
  violent force in a straight line, followed by a
  region of mixed motion and finally ends
  returning to natural motion, vertically down.

11
Galileos Thought Experiment
12
Galileos Insight

• A projectile near the earths surface has
• TWO INDEPENDENT MOTION COMPONENTS
• HORIZONTAL Constant velocity (Doesnt change)
• VERTICAL Subject to acceleration due to gravity
  (Varies over time)

13

• Two baseballs are pitched horizontally from the
  same height but at different speeds. The faster
  ball crosses home plate within the strike zone,
  but the slower ball is below the batters knees.
  Why does the faster ball not fall as far as the
  slower one?

14
Projectile Motion

• What are the two factors that affect projectile
  motion?

15
Angle and Velocity
16
g Acceleration due to gravity 9.8m/s2 x
distance in the x direction, vox initial
velocity in x direction t is time
vy final velocity in y direction voy, vy
initial and final velocity in y direction yo, y
initial and final distance in y direction
17
Off the table
18
Important Concept

• Treat the x component and the y component
  independently!

19
2D Motion Example I

• A stone is thrown horizontally 15-m/s from the
  top of a 44-m cliff.
• How far from the base of the cliff does the stone
  hit the ground?
• How fast is it moving the instant before it hits
  the ground?
• While it seems we are given very little
  information, this is enough to solve.

20
2D Motion Example I cont.

• How far from the base of the cliff does the stone
  hit the ground?
• We need to know how long it stays in the air for.
  This is determined by gravity y axis.

dy -44m v0y 0m/s ay -9.8m/s2 t x
dy v0yt ½at2 -44-m 0 -4.9 m/s2t2 t2
9.0s2 t 3.0s
21
2D Motion Example I cont.

• How far from the base of the cliff does the stone
  hit the ground?
• Time is the only variable that can and will be
  the same in both x and y axis.

v0x dx/t 15 m/s dx/3.0s dx 45.4m
dx x v0x 15m/s t 3.0s
22
2D Motion Example I cont.

• How fast is it moving the instant before it hits
  the ground?
• The final velocity is the addition of the x and y
  vector. Since the x is constant we need to find
  the y.

vfy2 voy2 2ad vfy2 0 2 -9.8m/s2
-44m vfy2 862.4m2/s2 vfy 29.4m/s
v0y 0m/s vfy x m/s ay -9.8m/s2 d -44m
23
2D Motion Example I cont.

• How fast is it moving the instant before it hits
  the ground?
• Add the vectors. (Pythagorean theory)

vfx 15m/s vfy 29.4m/s
vfy2 vfx2 vf2 (29.4-m/s)2 (15 m/s)2
vf2 vf2 1087.4m2/s2 vf 33.0-m/s
24
THEND