Calc10ex - 10 extra topic Projectile Motion Greg Kelly...

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Unformatted text preview: 10 extra topic: Projectile Motion Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002 Fort Pulaski, GA 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 = + v i j The initial position is: r o = + = i j → o v Newton’s second law of motion: Vertical acceleration f ma = 2 2 f d r m dt = → α o v 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 = → α o v 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 → α o v 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 → α 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 + ( 29 ( 29 cos sin o o v t v t α + + i j o v dr gt dt = -+ j → ( 29 ( 29 2 1 r cos sin 2 o o gt v t v t α = -+ + + j i j ( 29 ( 29 2 1 r cos sin 2 o o v t v t gt = +- i j Vector equation for ideal projectile motion: ( 29 ( 29...
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Calc10ex - 10 extra topic Projectile Motion Greg Kelly...

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