2. You say “Projectile” & I say “Amateurjectile… HONORS / FIZZIX 10/05/05
Daryl L Taylor, Fizzix Guy
Greenwich HS, CT

3. Projectile Properties?

4. Projectile Properties?

5. Projectile Properties?

6. Projectile Properties?

7. Projectile Properties?

8. Projectile Properties?
Hunter w/o Gravity!

9. Projectile Properties?
Hunter w/ Gravity!

10. Projectile Properties?
Hunter too SLOW!

11. Projectile Properties?
Bomb’s AWAY!

12. Hollywood Diversion!

13. NTQ
POP Quiz!

14. 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

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

16. Projectile Motion

17. Projectile Motion

18. Projectile Motion

19. Projectile Motion

20. Projectile Motion

21. Projectile Motion y x

22. 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

23. 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

24. Projectile Motion

25. 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

26. 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

27. 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!!!

28. 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!!!

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

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

31. Elliptical Orbits

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

33. What’s wrong with this picture ?
Answer: It never happens ! Only when
there is no gravity.

34. Why do projectiles fly in a parabola?

35. A History of Projectile Motion
Aristotle:
The canon ball travels in a
straight line until it lost its
‘impetus’.
Galileo:
- a result of Free Fall Motion
along y-yaxis and Uniform
Motion along x-axis.

36. Projectile Motion = Sum of 2 Independent Motions
1. Along x, the projectile travels with constant velocity.
vx=vxo x = vxot
Along y, the projectile travels in free-fall fashion.
vy = vyo – gt y = vyot – (1/2) gt2 , g= 9.8 m/s2
Projectile motion = a combination of uniform motion along x and
uniformly accelerated motion (free fall) along y.

37. What’s the similarity between a freely-falling ball and a projectile ?
uniform motion
Projectile
motion
vertical
motion x
A dropped ball falls in the same time as a ball shot horizontally.
Along the vertical, their motions are identical (uniformly
accelerated motion (free-fall).
Along the horizontal, notice the ball fired horizontally covers the
Same distance in the same unit time intervals (uniform motion along x)

38. v vy vx Velocity Components at various points of the Trajectory 
vertical component  vy v
Net velocity vx
Horizonal component
Above: Vectors are
added in geometric
Fashion.
Launch speed = Return Speed.
Speed is minimum at apex of parabolic trajectory.

39. At what angle do I launch for Maximum Range ?
Need to stay in air for the longest time,
and with the fastest horizontal velocity component
Answer: 45°

40. Everyday Examples of Projectile Motion
Baseball being thrown
Water fountains
Fireworks Displays
Soccer ball being kicked
Ballistics Testing