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Projectile Motion The properties of a projectile: – Parabolic motion is involved. – The horizontal component of acceleration of a projectile is zero. – The vertical acceleration of a projectile is constant because of gravity. – The horizontal and vertical motions of a projectile are independent, but they share the same time.

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Vertical Accelerated Motion (I) a = v 2 – v 1 Δt (II) Δd = v 1 Δt + ½a(Δt) 2 (III) Δd = ½ (v 1 + v 2 ) Δt (IV) v 2 2 = v 1 2 + 2aΔd (V) Δd = v 2 Δt - ½a(Δt) 2

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Horizontal Uniform Motion v av = Δd / ∆t

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ex. #1: A marble rolls off a table with a horizontal velocity of 1.93 m/s and onto the floor. The tabletop is 76.4 cm above the floor. Air resistance is negligible. a)Determine how long the marble is in the air. b)Calculate the range of the marble. c)Calculate the velocity of the marble when it hits the floor.

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ex #2: A projectile launcher is set at an angle of 45° above the horizontal and fires an object with a speed of 2.2 x 10 2 m/s. The object lands at the same height from which it was launched. Air resistance is negligible. Calculate the object’s: a)Time of flight b)Horizontal range c)Maximum height d)Velocity on impact with the ground

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ex #3: Prove using the equations: Δd y = v 1y Δt + ½a y (Δt) 2 and Δd x = v 1x Δt That the maximum range of a projectile is given by: Δd x = (v 1 ) 2 sin2θ g Hint: 2sinθcosθ = sin2θ

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