Solved: Vertical Motion An object is projected upward from ground level with an initial

Chapter 5, Problem 83

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Vertical Motion An object is projected upward from ground level with an initial velocity of 500 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. (b) Use the result in part (a) to find the position function and determine the maximum height attained by the object. (c) If the air resistance is proportional to the square of the velocity, you obtain the equation where feet per second per second is the acceleration due to gravity and is a constant. Find the velocity as a function of time by solving the equation (d) Use a graphing utility to graph the velocity function in part (c) if Use the graph to approximate the time at which the object reaches its maximum height. (e) Use the integration capabilities of a graphing utility to approximate the integral where and are those found in part (d). This is the approximation of the maximum height of the object. (f) Explain the difference between the results in parts (b) and (e). FOR FURTHER INFORMATION For more information on this topic, see What Goes Up Must Come Down; Will Air Resistance Make It Return Sooner, or Later? by John Lekner in Mathematics Magazine. To view this article, go to the website www.matharticles.com