Applying your knowledge of Inverse Functions. A ball is thrown vertically upward from the ground with velocity $s$. Find the maximum height $H$ of the ball as a function of $s$. Then find the velocity $s$ required to achieve a height of $H$. As usual, ignore air resistance, and assume that gravity causes a downward acceleration of 32 feet per second squared.
$H$ = .
$s$ = .
Hint: The velocity of the ball is $v(t)$ a function of time, $t$. It is given by $v(t) = s - 32t$. Integrate to get a function describing the height of the ball as a function of time.This also determines the height of the ball as a function of s. Use techniques you remember from Calculus I to maximize this function. For the second part, let H be some given height and set this equal to $H(s)$. Then use techniques of this chapter to find a value of s which achieves the height H. Remember that Mathematics and WeBWorK are case sensitive. So you need to use an upper case H and a lower case s.

You can earn partial credit on this problem.