Solved: PROBLEM 48EWhat Goes Up . . . (a) It is well known

Chapter 3, Problem 48E

(choose chapter or problem)

What Goes U p . . . (a) It is well known that the model in which air resistance is ignored, part (a) of Problem 36, predicts that the time \(t_{a}\) it takes the cannonball to attain its maximum height is the same as the time \(t_{d}\) it takes the cannonball to fall from the maximum height to the ground. Moreover, the magnitude of the impact velocity \(v_{i}\) will be the same as the initial velocity \(v_{0}\) of the cannonball. Verify both of these results.

(b) Then, using the model in Problem 37 that takes air resistance into account, compare the value of \(t_{a}\) with \(t_{d}\) and the value of the magnitude of \(v_{i}\) with \(v_{0}\). A root-finding application of a CAS (or graphic calculator) may be useful here.

Text Transcription:

t_a

t_d

v_i

v_0