chapter 5 projectile motion and satellites

Chapter 5Chapter 5Projectile Motion and Projectile Motion and

SatellitesSatellites

Projectile MotionProjectile Motion

Describe the motion of an object in Describe the motion of an object in TWO dimensionsTWO dimensions

Keep it simple by considering motion Keep it simple by considering motion close to the surface of the earth for close to the surface of the earth for the time beingthe time being

Neglect air resistance to make it Neglect air resistance to make it simplersimpler


The ball is in free fall vertically and moves at constant speed horizontally!!!


x

yHorizontal (x)

x v x t

Vertical (y)

y y0 v0y t 12gt 2

v y v0y gt


What happens when we add air What happens when we add air resistance?resistance?

Adds a new force on the ballAdds a new force on the ball The force is in the opposite direction to the The force is in the opposite direction to the

ball’s velocity vector and is proportional to ball’s velocity vector and is proportional to the velocity at relatively low speedsthe velocity at relatively low speeds

Need calculus to sort out the resulting Need calculus to sort out the resulting motionmotion

Lowers the angle for maximum rangeLowers the angle for maximum range


The trick to maximum range is just to The trick to maximum range is just to keep the object off the ground for as keep the object off the ground for as long as possible.long as possible.

This allows the horizontal motion to This allows the horizontal motion to be a maximum since be a maximum since x = vx = vxxtt

Make range longer by going higher Make range longer by going higher for your starting pointfor your starting point

Make range longer by having more Make range longer by having more velocityvelocity


Curvature of the earth enters into Curvature of the earth enters into our calculationsour calculations

If I start 5 m above the surface, it will still be at 5 m after one second if it is moving 8000 m/sec


Throw at 8000 m/sec

This is about 18,000 mph

Earth circumference is 25,000 miles

Takes 25000/18000 = 1.4 hours = 84 minutes

Higher altitude longer


Force of gravity on bowling ball is at 90o to velocity, so it doesn’t change the velocity!!!

If no air resistance, gravity doesn’t change speed of satellite, only direction!!!

Communications Communications SatellitesSatellites

Farther out you go, the bigger the Farther out you go, the bigger the circumference of the orbitcircumference of the orbit

It takes longer for the tripIt takes longer for the trip Also, gravity weakens by inverse Also, gravity weakens by inverse

square law the farther out you gosquare law the farther out you go Make the distance so that it takes 24 Make the distance so that it takes 24

hours for the orbithours for the orbit Satellite is stationary in the sky!!!Satellite is stationary in the sky!!!

The MoonThe Moon Distance is about 240,000 milesDistance is about 240,000 miles Takes 27.3 days to make an orbitTakes 27.3 days to make an orbit

Elliptical OrbitsElliptical Orbits

Give the object a speed a bit greater Give the object a speed a bit greater than 8 km/sec and the orbit will be than 8 km/sec and the orbit will be ellipticalelliptical


Sum of distances from foci to point on the ellipse is a constant!!!

Kepler’s LawsKepler’s Laws

Each planet moves in an elliptical orbit Each planet moves in an elliptical orbit with the sun at one focus of the ellipse.with the sun at one focus of the ellipse.

The line from the sun to any planet The line from the sun to any planet sweeps out equal areas of space in sweeps out equal areas of space in equal time intervalsequal time intervals

The squares of the periods of the The squares of the periods of the planets are proportional to the cubes of planets are proportional to the cubes of their average distances from the suntheir average distances from the sun

Kepler’s LawsKepler’s Laws

Energy ConservationEnergy Conservation

Escape SpeedEscape Speed

Throw at > 11.2 km/sec and ball escapes the pull of the earth!!!

chapter 5 projectile motion and satellites

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