1. Chapter 5 Projectile & Satellite Motion
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2. Projectile Motion
A ball thrown across the room follows an arced trajectory.
Example of projectile motion, which combines horizontal and vertical motion.
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3. Projectile Motion
Projectile motion combines uniform horizontal motion with freefall vertical motion.
Note: Use this concept in lab experiment entitled “Projectiles”
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4. Uniform Horizontal Motion1 2 3 4 5
Equal
Distances
Arbitrary
Rolling ball (with no friction) is an example of uniform motion.
Velocity of the ball is constant so distance between “frames” (equal time between frames).
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5. Accelerating Vertical Falling
1 (Release) 1 1 2
Falling is an example of accelerating motion. 4 3
Total distance from point of release increases in the ratios 1:4:9:16:25:… or 12:22:32:42:52… 3 9
Distance between frames increases as 1:3:5:7:9…. 5 16 4 7
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6. Projectile Motion 1 2 3 4 1
Arbitrary 5 3
Ball rolling off of a table combines horizontal and vertical motion.
Falling starts with frame #4, vertical distances increasing as 1:3:5:7:…
Horizontal distances equally spaced as with uniform motion.
Frames #4 to #7 are projectile motion. 6 5 7 7

7. Check Yourself
At the instant a cannon fires a cannonball horizontally over a level range, another cannonball held at the side of the cannon is released and drops to the ground.
Which strikes the ground first?
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8. Demo: Fall and Fire One ball is released and falls straight down.1 1
FIRE
One ball is released and falls straight down.
Other ball is fired horizontally.
At all times the balls are at the same height.
Hit the ground at the same time. 1 2 2 3 3 3 5 4 4
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9. Movie: Shoot the Monkey
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10. Projectiles Launched at an Angle
With no gravity, projectile would follow a straight line.
Due to gravity, projectile falls beneath this line, just as if released from rest.
No Gravity
With
Gravity
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11. Parabolic Arc Up and down motion is symmetric, as shown.4 1
Arbitrary 3 5 3
Arbitrary 2 6
Up and down motion is symmetric, as shown.
Frame #4 is highest point of the parabolic arc of projectile motion. 5 7 1 7
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12. Maximum Range Maximum range is at 45 degrees
(when air resistance is negligible).
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13. Demo: Trebuchet
Trebuchet is a type of catapult popular in the 13th century.
45 degrees
Warwolf
Release
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14. Movie: Trebuchet
Contestant in annual pumpkin throwing contest, Punkin Chukin
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15. Projectile Motion with Drag
Range reduced by air resistance.
Shape of the arc is changed.
Object lands at steeper angle.
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16. Distance Fallen
From Table 3.3 (page 47) we know that distance fallen in one second is
5 meters.
This distance fallen is the same whether falling straight down or in projectile motion.
0.5 s
5 meters
1.0 s
1.5 s
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17. Projectile Motion & Curvature
For initial speeds that are faster and faster, the range of the projectile is farther and farther.
For very large speeds, the curvature of Earth starts to be noticeable.
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18. Earth’s Curvature
Curvature of the Earth is about 5 meters over a distance of 8000 meters (which is about 5 yards over 5 miles).
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19. Missing the Ground
Suppose you throw a ball at a speed of 8000 m/s (about 18,000 mph).
After one second, ball travels 8000 meters and falls 5 meters.
In that distance, Earth curves by same amount (5 meters).
If nothing stops the ball, what happens?
8000 m
5 m
Curvature
NOT to
Scale
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20. Newton’s Mountain
Newton drew a similar illustration, picturing cannons firing from a tall mountain.
If a cannon was powerful enough, the cannonball would orbit Earth.
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21. Orbits and Centripetal Force
Gravity provides the centripetal force required for a satellite to move in a circle.
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22. Check Yourself
Satellites orbit at least 150 km (about 100 miles) above the surface of Earth because:
There is almost no gravity at that altitude?
There is almost no air resistance?
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23. Getting into Orbit Rocket needs to lift above the atmosphere and then
fire thrusters to acquire the
required orbital speed of
about 8 kilometers per
second.
Returning to Earth,
air resistance slows the
spacecraft during reentry.
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24. Elliptical Orbits
For speeds higher than 8 km/s, the orbit is elliptical instead of circular.
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25. Escape Speed
If speed exceeds 11.2 km/s then object escapes Earth because gravity weakens (as object gets further away) and never slows the object enough to return it back towards Earth.
Hyperbolic
Circular
Elliptical
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