137_pdfsam_math 54 differential equation solutions odd

137_pdfsam_math 54 differential equation solutions odd -...

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Exercises 3.4 v ( t )=9 . 5 g 2 ( 1 e t/ 20 ) . Since x (0) = 0, integrating the above equation, we obtain x ( t )= t Z 0 v ( s ) ds = t Z 0 9 . 5 g 2 ( 1 e s/ 20 ) ds =9 . 5 g 2 ( s +20 e s/ 20 ) ± ± ± s = t s =0 . 5 g 2 ( t e t/ 20 20 ) 131 . 8 t + 2636 e t/ 20 2636 . The object reaches the end of the inclined plane when x ( t ) = 131 . 8 t + 2636 e t/ 20 2636 = 10 t 1 . 768 (sec) . 21. In this problem there are two forces acting on a sailboat: A constant horizontal force due to the wind and a force due to the water resistance that acts in opposition to the motion of the sailboat. All of the motion occurs along a horizontal axis. On this axis, we choose the origin to be the point where the hard blowing wind begins and x ( t ) denotes the distance the sailboat
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