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.
You can earn partial credit on this problem.