FER0506 - M 408L - Integral Calculus Final Exam Review May...

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Unformatted text preview: M 408L - Integral Calculus Final Exam Review May 6, 2009 Toics: Applications: Motion, Area, Volume (of solids, of paperweights, as dou- ble integrals) 1. Jim decides to go BASE jumping off an Austin building. Unfortunately, he hits the ground with a speed of 128 ft/sec. His acceleration was a constant -32ft/sec 2 . How high was the building? Solution: The question is asking about Jim’s initial position, i.e. p ( t ) when t = 0, so p (0). Identifying the information in the problem we have: a ( t ) =- 32 v (0) = 0 v ( t end ) =- 128 p (0) = answer p ( t end ) = 0 . Integrate acceleration to find velocity: Z- 32 dt =- 32 t + C. Integrate velocity to find position: Z- 32 t + Cdt =- 16 t 2 + Ct + D. Now we use the information from the problem to find C , the end time, and D . v (0) =- 32(0) + C = 0 , so C = 0. v ( t end ) =- 32( t end ) =- 128 , so t end = 4. p ( t end ) = p (4) =- 16(4 2 ) + D = 0 , so D = 256. Therefore, p (0) =- 16(0)+256 = 256. So the building is 256 ft high....
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This note was uploaded on 09/23/2009 for the course M 57420 taught by Professor Radin during the Fall '09 term at University of Texas at Austin.

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FER0506 - M 408L - Integral Calculus Final Exam Review May...

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