Homework 5 - AMS 361: Applied Calculus IV by Prof Y. Deng...

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1 AMS 361: Applied Calculus IV by Prof Y. Deng Homework 5 Assignment Date: Wednesday (0 3 /11/2009) Collection Date: Wednesday (03/18/2009) Grade: Each problem is worth 10 points. Problem 5.1 (Prob. 27, P. 107, Modified) Suppose that a projectile is fired straight upward from the surface of the earth with initial velocity 0 2/ vG M R < . Then its height y(t) above the surface satisfies the initial value problem 2 22 () dy GM dt y R =− + , (0) 0 y = , 0 (0) yv = . Compute the maximum altitude the projectile reaches and the time (from launch) for the projectile to reach the maximum altitude. Problem 5.2 (Prof Deng’s fun problem, modified) On a straight stretch of road of length ܮ there were two stop signs at the two ends. Assume you follow traffic laws: stop at these signs. Your poor car can accelerate at a constant ܽ and decelerate at another constant
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