Assume a coordinate system where the origin is the point where supply pack is released, the positive x axis is the direction the plane is flying and the positive y axis points downward. Assume the horizontal and vertical components of the air resistance are proportional to the square of the velocities. a) Develop a system of differential equations and initial conditions to model this system for x (t) and y(t). Clearly state any additional assumptions in your write-up. b) Using the appropriate model, and as engineers, using accuracy to the nearest foot rounding off at the end of the problem, determine the horizontal distance the pack travels assuming The plane altitude is 1000 feet above the ground, the plane's speed is constant at 300 miles per hour, the proportionality constant for air resistance is k = 0.0053 in the correct units, and the pack weighs 256 pounds. supply pack