What Goes Up . . . In Problem 16 let ta be the time it takes the cannonball to attain its maximum height and let td be the time it takes the cannonball to fall from the maximum height to the ground. Compare the value of ta with the value of td and compare the magnitude of the impact velocity vi with the initial velocity v0. See Problem 48 in Exercises 3.1. A root-finding application of a CAS might be useful here. [Hint: Use the model in Problem 15 when the cannonball is falling.]
REFERENCE: Problem 48 in Exercises 3.1
What Goes Up . . . (a) It is well known that the model in which air resistance is ignored, part (a) of Problem 36, predicts that the time ta it takes the cannonball to attain its maximum height is the same as the time td it takes the cannonball to fall from the maximum height to the ground. Moreover, the magnitude of the impact velocity vi will be the same as the initial velocity v0 of the cannonball. Verify both of these results.
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