Math1011_Prelim2A - Math1011 Spring 2003 II-A1 A child...

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Math1011 Spring 2003 II-A1 A child releases a balloon from a point A on the ground. As the balloon rises vertically, the child walks in a straight path away from A. How are the three distances between point A, the balloon, and the child related? Use your answer above to find the rate at which the distance between the child and the balloon is changing three seconds after the balloon is released. Assume the balloon is rising at a constant rate of 5 ft/sec and the child is walking at a constant rate of 1 ft/sec. If the child stops walking after 4 seconds and watches the balloon rise, how fast is the distance between them changing?
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Math1011 Spring 2003 A1 A child releases a balloon from a point A on the ground. As the balloon rises vertically, the child walks in a straight path away from A. How are the three distances between point A, the balloon, and the child related? Point A, the balloon, and the child form a triangle. 2 2 z x y = + 2 Point A child balloon z y x Use your answer above to find the rate at which the distance between the child and the balloon is changing three seconds after the balloon is released. Assume the balloon is rising at a constant rate of 5 ft/sec and the child is walking at a constant rate of 1 ft/sec. 2 2 2 2 2 2 d d d dt dt dt dz dt take derivative with respect to time 2 2 2 solve for 2 2 2(3)(1) 2(15)(5) 5.1 /sec 2 2 234 dy dx dz dt dt dt dy dx dt dt dz dt x y z x y z x y z x y ft z + = + = + = + + = = 2 2 2 sec sec sec sec 2 2 3sec 1 3 1 3sec 5 15 5 3 15 234 ft ft dx dt ft dy ft dt z x y x ft y f z f = + = = = = = = = + = t eet If the child stops walking after 4 seconds and watches the balloon rise, how fast is the distance between them changing? 2 2 2 2 2 2 d d d dt dt dt dz dt take derivative with respect to time 2 2 2 solve for 2 2 2(4)(0) 2(20)(5) 4.9 /sec 2 2 416 dy dx dz dt dt dt dy dx dt dt dz dt x y z x y z x y z x y ft z + = + = + = + + = = 2 2 2 sec sec sec sec 2 2 4sec 1 4 0 (child stops!) 4sec 5 20 5 4 20 416 ft ft dx dt ft dy ft dt z x y x f y f z feet = + = = = = = = = + = t t (Doc #011p.39.01t)
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Math1011 Spring 2007 A2 A helium balloon contains 1000 cubic feet of natural gas at a pressure of 5 lb / sq in. Find the rate of change of the volume of gas if the pressure decreases at the rate of 0.05 lb / sq in. per second. You should assume Boyle’s law which says “Pressure times Volume is constant.” Simplify your numerical answer as much as possible.
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Math1011 Spring 2007 A2 A helium balloon contains 1000 cubic feet of natural gas at a pressure of 5 lb / sq in. Find the rate of change of the volume of gas if the pressure decreases at the rate of 0.05 lb / sq in. per second. You should assume Boyle’s law which says “Pressure times Volume is constant.” Simplify your numerical answer as much as possible.
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