Chapter 5 Projectile Motion and Satellites. Projectile Motion. Describe the motion of an object in TWO dimensions Keep it simple by considering motion close to the surface of the earth for the time being Neglect air resistance to make it simpler. Projectile Motion.
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Describe the motion of an object in TWO dimensions
Keep it simple by considering motion close to the surface of the earth for the time being
Neglect air resistance to make it simpler
The ball is in free fall vertically and moves at constant speed horizontally!!!
Adds a new force on the ball
The force is in the opposite direction to the ball’s velocity vector and is proportional to the velocity at relatively low speeds
Need calculus to sort out the resulting motion
Lowers the angle for maximum rangeProjectile Motion
The trick to maximum range is just to keep the object off the ground for as long as possible.
This allows the horizontal motion to be a maximum since x = vxt
Make range longer by going higher for your starting point
Make range longer by having more velocityProjectile Motion
Curvature of the earth enters into our calculations the ground for as long as possible.Satellites
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!!!
It takes longer for the trip
Also, gravity weakens by inverse square law the farther out you go
Make the distance so that it takes 24 hours for the orbit
Satellite is stationary in the sky!!!Communications Satellites
Takes 27.3 days to make an orbitThe Moon
Give the object a speed a bit greater than 8 km/sec and the orbit will be ellipticalElliptical Orbits
Sum of distances from foci to point on the ellipse is a constant!!!
Each planet moves in an elliptical orbit with the sun at one focus of the ellipse.
The line from the sun to any planet sweeps out equal areas of space in equal time intervals
The squares of the periods of the planets are proportional to the cubes of their average distances from the sunKepler’s Laws
Throw at > 11.2 km/sec and ball escapes the pull of the earth!!!