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42 Cards in this Set

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PROJECTILE

DEFINITION
ANY OBJECT THAT IS PROJECTED BY SOME MEANS AND CONTINUES IN MOTION BY ITS OWN INERTIA
HORIZONTAL COMPONENT
OF PROJECTILE VELOCITY

(NEGATING FRICTION)
-NO HORIZONTAL FORCE, VELOCITY IS CONSTANT

-MOVES FROM OWN INERTIA

-COVERS EQUAL DISTANCES IN EQUAL INTERVALS OF TIME
VERTICAL COMPONENT
OF PROJECTILE VELOCITY
-EXACTLY THE SAME AS AN OBJECT FALLING FREELY DOWN

-FASTER OBJECT FALLS, GREATER DISTANCE COVERED EACH SUCCESSIVE SECOND

-MOVING UPWARD THEN VERTICAL DISTANCES TRAVELED DECREASE W/ TIME ON THE WAY UP
CURVED PATH OF PROJECTILE

(NEGATING AIR DRAG)
-COMBINATION OF HORIZONTAL/VERTICAL MOTION

-COMPLETELY INDEPENDANT OF EACH OTHER

-CONSTANT HORIZONTAL VELOCITY IS NOT AFFECTED BY VERTICAL FORCE OF GRAVITY
PROJECTILES LAUNCHED HORIZONTALLY
-HORIZONTAL COMPONENT OF VELOCITY DOESN'T CHANGE AS OBJECT MOVES FORWARD

-TRAVELS SAME HORIZONTAL DISTANCE IN EQUAL TIMES, AS IF IT WERE ROLLING ON TABLE

-NO GRAVITATIONAL FORCE ACTING HORIZONTALLY

-GRAVITY ACTS DOWNWARD, SO GRAVITATION IS DOWNWARD

-VERTICAL POSITIONS BECOME FARTHER APART WITH TIME

-VERTICAL DISTANCES SAME AS IF BALL WAS DROPPED
PARABOLA

DEFINITION
TRAJECTORY OF A PROJECTILE THAT ACCLERATES ONLY IN THE VERTICAL DIRECTION WHILE MOVING AT A CONSTANT HORIZONTAL VELOCITY
PROJECTILES LAUNCHED AT ANGLE
-IF NO GRAVITY THEN WOULD FOLLOW STRAIGHT LINE PATH

-FALLS BENEATH STRAIGHT LINE PATH UNTIL IT HITS GROUND

-VERTICAL DISTANCE FALLS UNDERNEATH STRAIGHT LINE IS THE SAME AMOUNT IT WOULD FALL IF DROPPED
FORMULA FOR DISTANCE PROJECTILE FALLS
d = ½ gt²

g = 10 m/s

d = ½ (10 m/s) t²

d = 5t²
PROJECTILES WITH SAME LAUNCHING SPEED AND DIFFERENT ANGLES
-REACH DIFFERENT ALTITUDES

-HAVE DIFFERENT HORIZONTAL RANGES

-SAME RANGE IS OBTAINED FROM TWO DIFFERENT LAUNCHING ANGLES WHEN THE ANGLES ADD UP TO 90˚

-SMALLER ANGLE OBJECT RAMAINS IN AIR FOR SHORTER TIME
PROJECTILES WITH SAME LAUNCHING SPEED AND DIFFERENT ANGLES

EXAMPLE
-OBJECT THROWN WITH 60˚ WILL HAVE SAME RANGE IF THROWN FROM 30˚
ANGLE WITH MAXIMUM PROJECTILE RANGE
45˚
PROJECTILES LAUNCHED AT ANGLE
-IF NO GRAVITY THEN WOULD FOLLOW STRAIGHT LINE PATH

-FALLS BENEATH STRAIGHT LINE PATH UNTIL IT HITS GROUND

-VERTICAL DISTANCE FALLS UNDERNEATH STRAIGHT LINE IS THE SAME AMOUNT IT WOULD FALL IF DROPPED
FORMULA FOR DISTANCE PROJECTILE FALLS
d = ½ gt²

g = 10 m/s

d = ½ (10 m/s) t²

d = 5t²
PROJECTILES WITH SAME LAUNCHING SPEED AND DIFFERENT ANGLES
-REACH DIFFERENT ALTITUDES

-HAVE DIFFERENT HORIZONTAL RANGES

-SAME RANGE IS OBTAINED FROM TWO DIFFERENT LAUNCHING ANGLES WHEN THE ANGLES ADD UP TO 90˚

-SMALLER ANGLE OBJECT RAMAINS IN AIR FOR SHORTER TIME
PROJECTILES WITH SAME LAUNCHING SPEED AND DIFFERENT ANGLES

EXAMPLE
-OBJECT THROWN WITH 60˚ WILL HAVE SAME RANGE IF THROWN FROM 30˚
ANGLE WITH MAXIMUM PROJECTILE RANGE
45˚
PROJECTILES LAUNCHED AT ANGLE
VERTICLE TIME
-A PROJECTILE WILL RISE TO ITS MAXIMUM HEIGHT IN THE SAME TIME IT TAKES TO FALL FROM THAT HEIGHT
(NEGATING AIR DRAG)

-DECELERATION BY GRAVITY WHILE GOING UP IS SAME AS ACCELERATION BY GRAVITY COMING DOWN
SATELLITE

DEFINITION
-PROJECTILE THAT FALLS AROUND THE EARTH INSTEAD OF INTO IT.
SATELLITE CHARACTERISTICS

EXPLANATION
-SPEED MUST BE GREAT ENOUGH TO MAKE FALLING DISTANCE MATCH CURVATURE OF THE EARTH
CURVATURE OF EARTH
-DROPS A VERTICAL DISTANCE OF 5 METERS FOR EVERY 8000 METERS TANGENT TO THE SURFACE
SATELLITE SPEED
8 km PER SECOND

(29000 km/hr or 18000 mph)
SATELLITE W/ CIRCULAR ORBIT
-ALWAYS MOVES IN A DIRECTION PERPINDICULAR TO GRAVITY

-NO CHANGE IN SPEED OCCURS, JUST CHANGE IN DIRECTION
SATELLITE DISTANCE/TIME
-CLOSE TO EARTH
90 MINUTE ORBIT

-HIGHER ALTITUDES
ORBITAL SPEED IS LESS
PATH (DISTANCE) IS MORE
PERIOD IS LONGER
SPEED FOR SATELLITE IN ORBIT

FORMULA
v = √GM/d

(G IS UNIVERSAL GRAVITATIONAL CONSTANT

(M IS MASS OF THE EARTH)

(d IS DISTANCE OF SATELLITE FROM CENTER OF THE EARTH)
PERIOD OF SATELLITE MOTION

FORMULA
T = 2Π√d³/GM

(G IS UNIVERSAL GRAVITATIONAL CONSTANT

(M IS MASS OF THE EARTH)

(d IS DISTANCE OF SATELLITE FROM CENTER OF THE EARTH)
ELLIPSE

DEFINITION
-OVAL PATH

-SPECIFIC CURVE

-CLOSED PATH TAKE BY A POINT THAT MOVES SO THAT THE SUM OF ITS DISTANCES FROM TWO FIXED POINTS (FOCI) IS CONSTANT
FOCI

DEFINITION
TWO FIXED POINTS
ELLIPTICAL ORBIT

CHARACTERISTICS
-SPEED VARIES

-SATELLITE OVERSHOOTS A CIRCULAR PATH AND MOVES AWAY FROM EARTH

-LOSES SPEED AGAINST FORCE OF GRAVITY

-REGAINS SPEED AS IT FALLS BACK TOWARD THE EARTH

-REJOINS PATH WITH SAME INITIAL SPEED

-ALL ELLIPSES HAVE EARTH CENTER AS ONE FOCUS
PROJECTILE PATH RELATIONSHIP TO ELLIPSE
PARABOLIC PATH OF A PROJECTILE IS A TINY SEGMENT OF A SKINNY ELLIPS THAT EXTENDS WITHIN AND JUST BEYOND THE CENTER OF THE EARTH
KEPLERS FIRST LAW OF PLANETARY MOTION
THE PATH OF EACH PLANET AROUND THE SUN IS AN ELLIPSE WITH THE SUN AT ONE FOCUS
KEPLERS SECOND LAW OF PLANETARY MOTION
THE LINE FROM THE SUN TO ANY PLANET SWEEPS OUT EQUAL AREAS OF SPACE IN EQUAL TIME INTERVALS

-TRIANGULAR AREA COVERED DURING A MONTH WHEN A PLANET IS ORBITING FAR AWAY FROM THE SUN IS EQUAL TO THE AREA WHEN THE PLANET IS CLOSER.
KEPLERS THIRD LAW OF PLANETARY MOTION
THE SQUARE OF THE ORBITAL PERIOD OF A PLANET IS DIRECTLY PROPORTIONAL TO THE CUBE OF THE AVERAGE DISTANCE OF THE PLANET FROM THE SUN

(T² ~ r³ FOR ALL PLANETS)
SATELLITE ORBIT VS GRAVITY
-MOVES SLOWER AGAINST THE GRAVITATIONAL FIELD

-MOVES QUICKER WITH THE GRAVITATIONAL FIELD
ENERGY CONSERVATION AND SATELLITE MOTION

CIRCULAR ORBIT
-A SATELLITE ALWAYS HAS KE AND PE

-IN CIRCULAR ORBITS DISTANCE BETWEEN SATELLITE AND THE CENTER OF ATTRACTING BODY DOESN'T CHANGE

-PE IS THE SAME EVERYWHERE IN ORBIT

-BY CONSERVATION OF ENERGY IF PE DOENT CHANGE THEN KE DOESNT EITHER
ENERGY CONSERVATION AND SATELLITE MOTION

ELLIPTICAL ORBIT
-BOTH SPEED AND DISTANCE VARY

-PE IS GREATEST WHEN SATELLITE IS FAR AWAY, LEAST WHEN IT'S CLOSEST

-KE WILL BE LEAST WHEN PE IS MOST, AND MOST WHEN PE IS LEAST

-EVERY POINT IN THE ORBIT THE SUM OF PE AND KE ARE THE SAME

-AT ALL POINTS ALONG THE ORBIT (EXCEPT THE APOGEE AND PERIGEE) A COMPONENT OF GRAVITATIONAL FORCE PARALLEL TO THE DIRECTION OF MOTION THE SATELLITE
APOGEE

DEFINITION
SATELLITE IS FARTHEST AWAY FROM MAIN MASS
PERIGEE
WHEN SATELLITE IS CLOSEST TO CENTER MASS
ENERGY CONSERVATION AND SATELLITE MOTION

EXPLANATION
WHEN THE SATELLITE GAINS ALTITUDE AND MOVES AGAINST ITS COMPONENT, ITS KE SPEED DECREASE

ONCE PAST THE APOGEE THE SATELLITE MOVES IN THE SAME DIRECTION AS THE COMPONENT, THE SPEED AND KE INCREASE
ESCAPE SPEED

DEFINITION
CRITICAL STARTING SPEED THAT PERMITS A PROJECTILE TO OUTRUN GRAVITY AND TO ESCAPE EARTH
ESCAPE VELOCITY

DEFINITION
ESCAPE SPEED PLUS DIRECTION
ESCAPE SPEED

MEASUREMENT
11.2 km/sec
ESCAPE SPEED ENERGY
62 MILLION JOULES PER KILOGRAM OF LOAD