2.5 The height of a ball that is thrown straight up with a certain force is a function of the time (t) from which it is released given by f(t) ¼ %0.5gt2 þ 40t (where g is a constant determined by gravity).

a. How does the value of t at which the height of the ball is at a maximum depend on the parameter 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 g ¼ 32, but this value varies somewhat around the globe. If two locations had gravitational constants that differed by 0.1, what would be the difference in the maximum height of a ball tossed in the two places?