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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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B2.2. Projectiles follow curved (parabolic) paths know as trajectories These paths are the result of two, independent motions Horizontally, the.

B2.2. Projectiles follow curved (parabolic) paths know as trajectories These paths are the result of two, independent motions Horizontally, the.

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