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Unformatted text preview: 100 2 + b 2 ( t ) = c 2 ( t ) , (1) so dierentiating this equation with respect to t , 2 b ( t ) b ( t ) = 2 c ( t ) c ( t ) . Solving for b ( t ), we have b ( t ) = c ( t ) c ( t ) b ( t ) , so at the time t ? of interest it follows that b ( t ? ) = c ( t ? ) c ( t ? ) b ( t ? ) = 300 600 b ( t ? ) . In order to determine the missing value b ( t ? ) we note that equation (1) holds for all time, and so in particular it holds for t = t ? . That is, 100 2 + b 2 ( t ? ) = c 2 ( t ? ) = 300 2 , so b ( t ? ) = 300 2-100 2 = 80000 . It follows that b ( t ? ) = 300 600 80000 = 180000 200 2 = 450 2 ft/hr . 2...
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- Fall '10