Homework-5

# Homework-5 - and decelerate at another constant . Now,...

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1 AMS 361: Applied Calculus IV by Prof Y. Deng Homework 5 Assignment Date: Wednesday (10/14/2009) Collection Date: Wednesday (10/28/2009) Quiz-2 on 10/21/2009 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 ݒ √ଶீெ . Then its height ݕሺݐሻ above the surface satisfies the initial value problem ݕ ᇱᇱ ൌെܩܯ/ሺݕ൅ܴሻ ݕሺ0ሻൌ0 ݕ Ԣ ሺ0ሻൌݒ 0 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
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Unformatted text preview: and decelerate at another constant . Now, someone wants to install a 3 rd stop sign in-between (not overlapping) the previous two. Compute the shortest time to travel between the two original stop signs and the spot you install the 3 rd to enable this, under two conditions: (1) no speed limit and (2) speed limit is . Problem 5.3 Check if the following three functions are linearly independent: 2, 3x , 5 8 Problem 5.4 (Prob 37, P. 159, 4E) Find the general solution of the following equation: 2 0 Problem 5.5 (Prob 40, P. 159, 4E) Find the general solution of the following equation: 9 12 4 0 Problem 5.6 (Prob 55, P. 160, 4E) Find the general solution of the following equation: 0...
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## This note was uploaded on 08/08/2010 for the course AMS 361 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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