Vertical Motion An object is dropped from a height of 400 feet. (a) Find the velocity of

Chapter 5, Problem 92

(choose chapter or problem)

Vertical Motion An object is dropped from a height of 400 feet. (a) Find the velocity of the object as a function of time (neglect air resistance on the object). (b) Use the result in part (a) to find the position function. (c) If the air resistance is proportional to the square of the velocity, then where feet per second per second is the acceleration due to gravity and is a constant. Show that the velocity as a function of time is by performing the following integration and simplifying the result. (d) Use the result in part (c) to find and give its interpretation. (e) Integrate the velocity function in part (c) and find the position of the object as a function of Use a graphing utility to graph the position function when and the position function in part (b) in the same viewing window. Estimate the additional time required for the object to reach ground level when air resistance is not neglected. (f) Give a written description of what you believe would happen if were increased. Then test your assertion with a particular value of Tractrix In Exercises 93 and 94, use the equation of the tractrix y a sech a > 0.