Solved: Relief Supplies As shown in Figure 5.3.11, a plane

Chapter 5, Problem 5.1.116

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Relief Supplies As shown in Figure 5.3.11, a plane flying horizontally at a constant speed v0 drops a relief supply pack to a person on the ground. Assume the origin is the point where the supply pack is released and that the positive x-axis points forward and that positive y-axis points downward. Under the assumption that the horizontal and vertical components of the air resistance are proportional to and , respectively, and if the position of the supply pack is given by then its velocity is . Equating components in the vector form of Newtons second law of motion, gives (a) Solve both of the foregoing initial-value problems by means of the substitutions and separation of variables. [Hint: See the Remarks at the end of Section 3.2.] (b) Suppose the plane files at an altitude of 1000 ft and that its constant speed is 300 mi/h. Assume that the constant of proportionality for air resistance is and that the supply pack weighs 256 lb. Use a root-finding application of a CAS or a graphic