# Calc10_4 - 10.4 Projectile Motion Fort Pulaski GA Photo by...

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10.4 Projectile Motion Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002 Fort Pulaski, GA

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One early use of calculus was to study projectile motion . In this section we assume ideal projectile motion: Constant force of gravity in a downward direction Flat surface No air resistance (usually)
We assume that the projectile is launched from the origin at time t =0 with initial velocity v o . o v Let o o v = v ( 29 ( 29 then cos sin o o o v v α α = + v i j The initial position is: r 0 0 0 o = + = i j α

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o v α Newton’s second law of motion: Vertical acceleration f ma = 2 2 f d r m dt =
o v α Newton’s second law of motion: The force of gravity is: Force is in the downward direction f ma = f mg = - j 2 2 f d r m dt =

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o v α Newton’s second law of motion: The force of gravity is: f ma = f mg = - j 2 2 f d r m dt = mg = - j 2 2 d r m dt
o v α Newton’s second law of motion: The force of gravity is: f ma = f mg = - j 2 2 f d r m dt = mg = - j 2 2 d r m dt

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2 2 d r g dt = - j Initial conditions: r r v when o o dr t o dt = = = 2 o 1 r v r 2 o gt t = - + + j 2 1 r 2 gt = - j 0 + ( 29 ( 29 cos sin o o v t v t α α + + i j o v dr gt dt = - + j
( 29 ( 29 2 1 r cos sin 0 2 o o gt v t v t α α = - + + + j i j ( 29 ( 29 2 1 r cos sin 2 o o v t v t gt α α = + - i j Vector equation for ideal projectile motion:

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