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Unformatted text preview: tangential and normal components. 5 FORMULA SHEET 1. The trajectory of an object thrown in the air is given by the formula: r ( t ) = r + v t1 2 g t 2 where g = (0 , 32) , r is the initial position and v is the initial velocity. Additionally v =  v  is the initial speed. 2. The arc length of a curve given by the parametrization r ( t ) , a t b, is equal to: b a  r ( t )  dt. 3. The tangential and normal components of the acceleration for the trajectory given by the parametrization r ( t ) . The acceleration has a decomposition a ( t ) = v ( t ) T ( t ) + v ( t )  T ( t )  N ( t ) , where v ( t ) =  r ( t )  , T ( t ) = 1  r ( t )  r ( t ) and N ( t ) = 1  T ( t )  T ( t ) ....
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 Spring '08
 RONEVANS
 Math, Multivariable Calculus

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