1. 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

2. Projectile Motion
The ball is in free fall vertically and moves at constant speed horizontally!!!

3. Projectile Motion

4. Projectile Motion

5. Projectile Motion

6. Projectile Motion

7. Projectile Motion

8. Projectile Motion y x

9. Projectile Motion What happens when we add air resistance?
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 range

10. Projectile 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 velocity

11. Projectile Motion

12. Satellites Curvature of the earth enters into our 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

13. Satellites 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

14. Satellites
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!!!

15. Communications Satellites
Farther out you go, the bigger the circumference of the orbit
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!!!

16. The Moon Distance is about 240,000 miles
Takes 27.3 days to make an orbit

17. Elliptical Orbits
Give the object a speed a bit greater than 8 km/sec and the orbit will be elliptical

18. Elliptical Orbits

19. Elliptical Orbits
Sum of distances from foci to point on the ellipse is a constant!!!

20. Kepler’s Laws
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 sun

21. Kepler’s Laws

22. Energy Conservation

23. Energy Conservation

24. Energy Conservation

25. Escape Speed
Throw at > 11.2 km/sec and ball escapes the pull of the earth!!!