Applying your knowledge of Inverse
Functions. A ball is thrown vertically upward from the ground with
velocity . Find the maximum height of the ball as a
function of . Then find the velocity required to achieve a
height of . As
usual, ignore air resistance, and assume that gravity causes a
downward acceleration of 32 feet per second squared.
= .
= .
Hint: The velocity of the ball is a function of
time, . It is given by . 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 . 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.