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Math 1320 - Lab 11 uNiD: Name: Due: 11/21 READ BEFORE PROCEEDING: Today we will continue with some application problems in multivariate calculus. Don’t forget to write your reasoning (in COMPLETE and CONCISE sentences) behind your approach to each problem so that someone who has taken Math 1310 would understand what you are doing. Present your work in such a way that someone without access to the questions can read through your solutions and understand it. To achieve this, set-up the problem in your own words and describe NEATLY and LEGIBLY the procedures you take in solving the problem. Disjoint or unclear explanations may result in lost points. 1. A ball with mass 0.8 kg is thrown southward into the air with a speed of 30m/s at an angle of 30o to the ground. A west wind applies a steady force of 4 N to the ball in an easterly direction. Where does the ball land and with what speed? 2. Using Newton’s second law of motion, F = ma, and his law of gravitation , F=− GM m r, r3 show that the orbit of a planet around the sun is a plane curve. (Here F is the gravitational force on the planet, m and M are the masses of the planet and the sun, respectively, G is a constant, and r = |r|. (a) Equate the two expressions for F. What does the new equation say about the vectors a and r? What does a × r equal? d (b) Compute (r × v). What does your result say about r × v? dt