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Chapter 6
Projectile Motion
6-Jul-17
Physics 1 (Garcia) SJSU
Projectiles
• A projectile is any object that moves
through space where the only force acting
on the object is gravity.
• The path that a projectile follows is called
a trajectory.
6-Jul-17
Physics 1 (Garcia) SJSU
Projectile Motion
A ball thrown
across the room
follows an arced
trajectory.
Example of
projectile
motion, which
combines
horizontal and
vertical motion.
6-Jul-17
Physics 1 (Garcia) SJSU
Projectile Motion
Projectile motion
combines
uniform
horizontal motion
(constant
speed)with
freefall vertical
motion (constant
acceleration.
6-Jul-17
Physics 1 (Garcia) SJSU
Uniform Horizontal Motion
1
2
3
Equal
Distances
4
5
Arbitrary
Rolling ball (with no friction) is an example of uniform motion.
Velocity of the ball is constant so distance between “frames”
(equal time between frames) is constant.
6-Jul-17
Physics 1 (Garcia) SJSU
Accelerating Vertical Falling
1 (Release)
1
4
1
2
3
3
9
Falling is an example of accelerating
motion.
Total distance from point of release
increases in the ratios 1:4:9:16:25:…
or 12:22:32:42:52…
Distance between frames increases as
1:3:5:7:9….
5
16
4
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7
Physics 1 (Garcia) SJSU
Projectile Motion
1
2
3
4
1
5
Arbitrary
3
Ball rolling off of a table combines
horizontal and vertical motion.
Falling starts with frame #4, vertical
distances increasing as 1:3:5:7:…
Horizontal distances equally spaced as
with uniform motion.
Frames #4 to #7 are projectile motion.
6-Jul-17
Physics 1 (Garcia) SJSU
6
5
7
7
Check Yourself
At the instant a cannon fires a cannonball horizontally over
a level range, another cannonball held at the side of the
cannon is released and drops to the ground.
Which strikes the ground first?
6-Jul-17
Physics 1 (Garcia) SJSU
Demo: Fall and Fire
FALL
1
2
One ball is
released and falls
straight down.
Other ball is fired
3
horizontally.
At all times the
balls are at the
same height.
Hit the ground at
the same time.
1
FIRE
1
2
3
3
5
4
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4
Physics 1 (Garcia) SJSU
Movie: Shoot the Monkey
6-Jul-17
http://www.youtube.com/watch?v=cxvsHNRXLjw
Distance Fallen
From Table 3.3
(page 47) we know
that distance fallen
in one second is
5 meters.
This distance fallen is
the same whether
falling straight
down or in
projectile motion.
6-Jul-17
Physics 1 (Garcia) SJSU
0.5 s
5 meters
1.0 s
1.5 s
Projectile Motion & Curvature
For initial speeds that are faster and faster, the range of
the projectile is farther and farther.
For very large speeds, the curvature of Earth starts to be
noticeable.
6-Jul-17
Physics 1 (Garcia) SJSU
Projectiles Launched at an Angle
With no gravity,
projectile would
follow a straight line.
Due to gravity,
projectile falls
beneath this line,
just as if released
from rest.
6-Jul-17
Physics 1 (Garcia) SJSU
With
Gravity
Parabolic Arc
4
1
Arbitrary
3
3
5
Arbitrary
2
5
1
7
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6
Up and down motion is
symmetric, as shown.
Frame #4 is highest point
of the parabolic arc of
projectile motion.
Physics 1 (Garcia) SJSU
7
Maximum Range
Maximum range is at 45 degrees
(when air resistance is negligible).
6-Jul-17
Physics 1 (Garcia) SJSU
Demo: Trebuchet
Trebuchet is a type of catapult popular in the 13th century.
45 degrees
Warwolf
6-Jul-17
Release
Physics 1 (Garcia) SJSU
Movie: Trebuchet
Contestant in
annual pumpkin
throwing contest,
Punkin Chukin
6-Jul-17
Physics 1 (Garcia) SJSU
Projectile Motion with Drag
Range reduced by air resistance.
Shape of the arc is changed.
Object lands at steeper angle.
6-Jul-17
Physics 1 (Garcia) SJSU
Earth’s Curvature
Curvature of the Earth is about 5 meters
over a distance of 8000 meters (which is
about 5 yards over 5 miles).
6-Jul-17
Physics 1 (Garcia) SJSU
Missing the Ground
Suppose you throw a ball at a speed of 8000 m/s (about 18,000 mph).
After one second, ball travels 8000 meters and falls 5 meters.
In that distance, Earth curves by same amount (5 meters).
If nothing stops
the ball, what
happens?
8000 m
5m
NOT to
Scale
6-Jul-17
Physics 1 (Garcia) SJSU
Newton’s Mountain
Newton drew a
similar illustration,
picturing cannons
firing from a tall
mountain.
If a cannon was
powerful enough,
the cannonball
would orbit Earth.
6-Jul-17
Physics 1 (Garcia) SJSU
Orbits and Centripetal Force
Gravity provides the centripetal force
required for a satellite to move in a circle.
6-Jul-17
Physics 1 (Garcia) SJSU
Check Yourself
Satellites orbit at least 150 km (about 100
miles) above the surface of Earth because:
There is almost no gravity at that altitude?
There is almost no air resistance?
6-Jul-17
Physics 1 (Garcia) SJSU
Getting into Orbit
Rocket needs to lift above
the atmosphere and then
fire thrusters to acquire the
required orbital speed of
about 8 kilometers per
second.
Returning to Earth,
air resistance slows the
spacecraft during reentry.
6-Jul-17
Physics 1 (Garcia) SJSU
Elliptical Orbits
For speeds higher than 8 km/s, the orbit is
elliptical instead of circular.
6-Jul-17
Physics 1 (Garcia) SJSU
Escape Speed
If speed exceeds
11.2 km/s then
object escapes
Earth because
gravity weakens (as
object gets further
away) and never
slows the object
enough to return it
back towards Earth.
6-Jul-17
Hyperbolic
Circular
Elliptical
Physics 1 (Garcia) SJSU
End of Part I:
Mechanics
6-Jul-17
Physics 1 (Garcia) SJSU