Review: Free fall- object projected vertically up
Review: motion with constant acceleration
1. a = 0 case
Position, y
• Maximum height
H
0
v0
Æ no acceleration Æ velocity is constant Æ v = vo
v2
H= 0
2g
ttop
2ttop
Time, t
• Time to highest point
ttop =
Velocity, v
Time, t
−v0
Æ position vs. time Æ
v0
g
velocityÆ v = vo + a t, vo is the initial velocity at time t = 0 s
positionÆ if motion starts at xo = 0, with vo = 0 (initially at rest)
Æ x = ½ a t2
v0
g
if the motion is free-fall, then a = g = 10 m/s2
L-5 Projectile motion
Projectile Examples
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A projectile is an object that is thrown or struck or
shot and then travels under the influence of gravity
Not projectiles
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xo is the starting position
2. acceleration = a = constant
• Total time in air
ttotal = 2ttop = 2
x = x o + vo t,
Tennis ball
Golf ball
Football
Softball
Soccer ball
bullet
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Hockey puck or ball
Basketball
Volleyball
Arrow
Shot put
Javelin
These are all examples of things that are
projected, then go off under the
influence of gravity
Unintended projectile
Jet plane
Rocket
Car (unless it looses contact with ground)
catapult (before rock leaves)
slingshot (before rock leaves sling)
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Demonstration
force of
gravity
Æ The key to understanding
projectile motion is to realize
that gravity acts vertically
Æ gravity affects only the
vertical motion, not the
horizontal motion
• We can see that the
horizontal and vertical
motions are independent
• The red ball falls
vertically
• The yellow ball was
given a kick to the right.
• They track each other
vertically step for step
and hit the ground at the
same time
Galileo’s inclined plane experiments
NO!
YES
Hitting the target – aim high, not
directly at the target
In the absence of gravity a bullet
would follow a straight line forever.
With gravity it FALLS AWAY from
that straight line!
Life without gravity
Football without gravity
BULLSEYE!
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Basketball – without gravity
Path of the Projectile: parabola
Projectile motion – key points
Height
No gravity is good for kickers
falling
rising
g
v
projectile
v
Distance downfield
(range)
Vertical
velocity
1) The projectile has both a vertical and
horizontal component of velocity
2) The only force acting on the projectile
once it is shot is gravity (neglecting air
resistance)
3) At all times the acceleration of the
projectile is g = 10 m/s2 downward
4) The horizontal velocity of the projectile
does not change throughout the path
Horizontal velocity
Key points, continued
More key points
5) On the rising portion of the path gravity
causes the vertical component of velocity
to get smaller and smaller
6) At the very top of the path the vertical
component of velocity is ZERO
7) On the falling portion of the path the
vertical velocity increases
8) If the projectile lands at the same
elevation as its starting point it will have
the same vertical SPEED as it began with
9) The time it takes to get to the top of its
path is the same as the time to get from
the top back to the ground.
10)The range of the projectile (where it
lands) depends on its initial speed and
angle of elevation
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Maximum Range
• When an artillery shell is
fired the initial speed of
the projectile depends on
the explosive charge –
this cannot be changed
• The only control you have
is over the angle of
elevation.
• You can control the range
(where it lands) by
changing the angle of
elevation
• To get maximum range
set the angle to 45°
NEWTON
65°
y
45°
25°
x
15°
The ultimate projectile:
Putting an object into orbit
• Imagine trying to
throw a rock around
the world.
• If you give it a large
horizontal velocity,
it will go into orbit
around the earth!
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