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Projectile Motion

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Feeding the Monkey (Banana Gun) l Where does the zookeeper aim if he wants to hit the monkey? ( He knows the monkey will let go as soon as he shoots ! )

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Feeding the Monkey... l If there were no gravity, simply aim at the monkey r = r 0 r =v 0 t

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Feeding the Monkey... rvg r = v 0 t - 1 / 2 g t 2 l With gravity, still aim at the monkey! rg r = r 0 - 1 / 2 g t 2 Banana hits monkey!

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Projectile: An Object Moving Solely Under Influence of Gravity

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Horizontally Launched Projectile

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Projectile Motion

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Projectile Velocities

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Net Force in Freefall Horizontal Motion Vertical Motion Net Force NO YES – force of gravity – downward Acceleration NO YES – “g” is downward at about 10 m/s/s Velocity Constant Changing by about 10 m/s each second

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Independence of x & y Motions t (s)V y (m/s)Y (m) 000 1105 220 33045 44080 t10 t5t 2 X (m) 0 5 10 15 20 vxtvxt For V x = 5 m/s

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Projectile Launched at Angle

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Projectile Launched at Angle - 2

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Monkey Zookeeper

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Monkey – Zookeeper – No Gravity

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Monkey Zookeeper - Fast

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Monkey – Zookeeper - Slow

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Projectile Trajectories Complementary angles have equal ranges

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Satellite Motion l If superman threw a rock fast enough … it would orbit the earth (if there were no air resistance

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Satellite = Fast Projectile l Since the earth’s surface curves away from the horizontal by 5 m for every 8000 m tangent to the surface l V = 8000 m/s = 8 km/s

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Satellite Periods l For a satellite close to the Earth, the period (the time for a complete orbit about the Earth) is about 90 minutes. l For higher altitudes, the orbital speed is less, distance is more, and the period is longer. l For example, communication satellites located in orbit 5.5 Earth radii above the surface of the Earth have a period of 24 hours.

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