Quiz 1 - ௗ ൌ ߚݕሺߙ െ ݈݊ ݕ where obviously...

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1 AMS 361: Applied Calculus IV by Prof. Y. Deng Quiz 1 Wednesday (02/25/2009) at 8:05AM-9:25AM (1) Open Book and Open Own Lecture Notes; Calculators Allowed (2) Do Any Two of the Three Problems; Mark the Two Problems You Attempt; Will Only Grade the First Two if You Don’t Mark the Problems You Attempted (3) Each Problem Is Worth 7.5 Points (4) No Points for Guessing Work and for Solutions Without Appropriate Intermediate Steps; Partial Credits are Given only for Steps that are Relevant to the Solutions. SB ID: Class ID: Name: Problems To Grade? Score Remarks Q1-1 Q1-2 Q1-3 Total Score Q1-1 (7.5 points): Find the general solutions of the following two unrelated differential equations (3.5 Points for DE.1 and 4.0 Points for DE.2): DE.1: ሺݔ ൅ݔݕሻ݀ݔ െ ሺݔݕ ൅ ݕ ሻ݀ݕ ൌ 0 DE.2: ݕݕ ൅2ݔݕ ൅1ൌ0 Q1-2 (7.5 points): Solve DE: ௗ௬
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Unformatted text preview: ௗ௧ ൌ ߚݕሺߙ െ ݈݊ ݕሻ where, obviously, ߙ and ߚ are parameters independent of ݕ and ݐ . If ݕሺݐ ൌ 0ሻ ൌ ݕ ଴ and ݕሺݐ ՜ ∞ሻ ൌ ݕ ஶ , can you express ߙ and/or ߚ in terms of ݕ ଴ and ݕ ஶ ? If so, do it. Q1-3 (7.5 points): A man with a parachute jumps out of a “frozen” helicopter at height ܪ . During the fall, the man's drag coefficient is ݇ (with closed parachute) and ݊݇ (with open parachute) and air resistance is taken as proportional to velocity. The total weight of the man and his parachute is ݉. Take the initial velocity when he jumped to be zero. Gravitational constant is ݃. The man opens the parachute ݐ ଴ time after he jumps. Please find the total falling time and the speed he hits the group. Can you adjust the ݐ ଴ to enable the quickest fall and lightest hit on the ground?...
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This note was uploaded on 05/11/2009 for the course AMS 361 taught by Professor Staff during the Spring '08 term at SUNY Stony Brook.

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