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1 Projectile Motion

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2 Projectile An object that moves through the air only under the influence of gravity after an initial thrust For simplicity, we’ll use 9.8 m/s 2 for gravity. Trajectory – path of a projectile

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3 The vertical and horizontal components of a projectile are independent of each other If 1 ball were dropped and another ball launched forward from the same height, they would hit the ground at the same time.

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Video Break Mythbusters 4

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5 Force vectors for projectiles Draw both horizontal and vertical vectors

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Vertical Horizontal d = ½ gt 2 V = gt d = Vt V = d/t

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7 Horizontally launched cannonball

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8 Non-horizontally launched cannonball

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9 Vertical Component Distance d = V i t + ½ gt 2 *V i is 0, so it cancels! d = ½ gt 2 Velocity V f = V i + gt *V i is 0, so it cancels! V = gt

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10 Horizontal Component Distance d = Vt Velocity V = d/t

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11 Example) A stone is thrown horizontally at 15 m/s from the top of a cliff 44 m high. a) How long does it take to fall? d = ½ gt 2 44 = ½ (9.80)(t 2 ) 44 = 4.90( t 2 ) 8.9796 = t 2 t = 3.0 s 44m 15m/s

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12 Example) A stone is thrown horizontally at 15 m/s from the top of a cliff 44 m high. b) How far from the base of the cliff does it land? d = Vt d = (15)(3.0) d = 45 m d

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13 Example) A stone is thrown horizontally at 15 m/s from the top of a cliff 44 m high. c) What is its vertical speed when it hits the ground? V = gt V = (9.80)(3.0) V = 29.4 m/s

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14 Example 2) A ball is thrown at a horizontal speed of 18 m/s. It’s flight time is 4.6 seconds. How high does the ball go? d = ½ gt 2 d = ½ (9.80)(2.3 2 ) d = 25.92 m

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15 Example 2) A ball is thrown at a speed of 18 m/s. It rises and falls in 4.6 seconds. How far away does it land? d = Vt d = (18)(4.6) d = 82.8 m

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16 Example 2) A ball is thrown at a speed of 18 m/s. It rises and falls in 4.6 seconds. What is its vertical speed when it hits the ground? V = gt V = (9.8)(2.3) V = 22.54 m/s

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Projectile Motion I 11/7/14. Throwing a ball in the air On the way up: At the top of the throw: On the way down: velocity decreases acceleration stays.

Projectile Motion I 11/7/14. Throwing a ball in the air On the way up: At the top of the throw: On the way down: velocity decreases acceleration stays.

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