Transcript Free fall – faster, faster, faster

Projectile motion
X meets Y and a beautiful dance ensues
often leading to great destruction.
Projectiles
 A projectile has only one
force acting upon - the
force of gravity
 Examples: golf, soccer
ball, bullet, rock dropped,
javelin thrower …
The path (trajectory)
of a projectile is a parabola
Parabolic motion of a
projectile
Horizontal and vertical motion are
independent (90°)
 There are the two components of the projectile's
velocity – horizontal vX and vertical vY .
 The horizontal component of it’s velocity does not
change. vX is constant
Gravity is the
only force
Horizontal and vertical motion are
independent !
Package drop
 The package follows a parabolic path and remains directly
below the plane at all times
 The vertical velocity changes (faster, faster)
 The horizontal velocity is constant!
Trajectory and Range
 Maximum range
is at 45°
 Low and high
trajectory cover
the same
distance.
 30 and 60
 10 and 80
 25 and…
 Projectile motion Animation
 http://www.ngsir.netfirms.com/englishhtm/Thr
owABall.htm
 QT movie
 http://www.physicslab.co.uk/shoot.htm
vX is constant
vy changes
Component of
Motion
X Acceleration
Y Acceleration
X Velocity
Y Velocity
X Position
Y Position
Equation
History of science
 Projectile motion based on Aristotelian
principles.
"Four Mortars Firing Stones into the Courtyard
of a Fort" (c.1504), by Leonardo da Vinci (14521519)
Projectile motion depicted in Nova Scientia (1537), by
Niccolò Tartaglia (c.1500-1557)
"Judith Slaying Holofernes" (c. 1620), by Artemisia
Gentileschi (1593-1652)
A Treatise of the System of the World (published
posthumously, 1729) by Isaac Newton (1642-1727)
General 1-D Velocity Equation
X-Component of Velocity
Y-Component of Velocity
Projectile motion at an angle

Time for Peak of Projectile
 Maximum height
 Maximum Range
 Velocity and Position
Equations using Angular
Dependence
Experiment
What do you think? Which ball will hit the ground first?
a)
b)
c)
The left ball will hit first
The right ball will hit first
They will hit the ground at the same time.
Projectiles
Both balls hit the ground at the same time.
Why?
As soon as both balls are released by the
launcher, they are in "freefall.
The only force acting on both objects is gravity.
Both objects accelerate at the same rate, 9.8m/s2
Both objects covering the same distance at the
same rate and therefore hit the ground at the
same time
d = ½ gt2
t2 = 2d/g
Shoot the monkey!
Projectile
Circular Motion Principles for
Satellites
Satellites
 Sputnik 1958
 Satellites can be classified by their functions. Satellites are
launched into space to do a specific job.
 (Astronomy, weather, communication, navigation, remote
sensing, space exploration…)
http://collections.ic.gc.ca/satellites/english/engineer/copy/index.html
Orbits
 After a satellite is launched into space, it needs little to no power to
keep it moving
 The orbit is a combination of the satellite's velocity - the speed it is
traveling in a straight line - and the force of the Earth's gravitational
pull on the satellite.
 Communication satellites, TV
 High orbit - 35, 850 km above the Earth
 located directly above the equator -equatorial orbit
 G.E.O. which stands for Geostationary Orbit.
 Geostationary satellites like geosynchronous satellites take 24
hours to complete a rotation.
 Low Earth Orbit, or L.E.O. L.E.O. is 248 to 621 miles
high from earth. L.E.O. is good for weather, survey
and scientific satellites.
 There is also the P.O. which is the Polar Orbit. Polar
Orbit is another low earth orbit used for mapping,
navigation and surveillance.
 http://science.nasa.gov/realtime/
 http://www.lon-capa.org/~mmp/kap7/orbiter/orbit.htm