The height of a bullet that is fired straight up into the air with a certain force is a function of the time (t) from which it is released given by (where g is a constant determined by gravity). a. How does the value of t at which the height of the bullet is at a maximum depend on the value of g? b. Use your answer to part (a) to describe how maximum height changes as the parameter g changes. c. Use the envelope theorem to answer part (b) directly. d. On the Earth gravity varies somewhat around the globe. If the first of two locations had gravitational constant of 32 and the second has a gravity of 32.1, what is the difference between the maximum heights of a bullet fired in the two places? Prove that the envelope theorem would yield the same result.

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