11. [0.04/0.28 Points] DETAILS PREVIOUS ANSWERS An object is projected upward from ground level with an initial velocity of 300 feet per second. In this exercise, the goal is to analyze the motion of the object during its upward flight. (a) If air resistance is neglected, find the velocity of the object as a function of time. Use a graphing utility to graph this function. v ( t ) = (b) Use the result of part (a) to find the position function. 5 ( t ) = Determine the maximum height (in ft) attained by the object. hmax = (c) If the air resistance is proportional to the square of the velocity, you obtain the equation = - (32 + KV 2 ) where -32 feet per second per second is the acceleration due to gravity and k is a constant. Find the velocity as a function of time by solving the equation 4 32 + Ky ? = - / dt. v ( t ) = to = (d) Use a graphing utility to graph the velocity function v(t) in part (c) for k = 0.002. Use the graph to approximate the time to (in s) at which the object reaches its maximum height. (Round your answer to two decimal places.) (e) Use the integration capabilities of a graphing utility to approximate the integral ( V (t ) at h =[ where v(t) and to are those found in part (d). This is the approximation of the maximum height (in ft) of the object. (Round your answer to two decimal places.) (f) Explain the difference between the results in parts (b) and (e)