The height, in meters, of a stream of water projected upward from a fountain is…
MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The height, in meters, of a stream of water projected upward from a fountain is modeled for t≥0 seconds by the function
s(t)=te−t/3.
Assume the model is valid until the water returns to ground level.
(a) Find s′(t) and determine all critical times t>0 for which s′(t)=0.
(b) Determine the sign of s′(t) on the intervals determined by the critical time from part (a). Show analytical work supporting each sign determination.
(c) Give the exact time at which the water stream reaches its local maximum height, and compute that height.
(d) Interpret the practical meaning of your result from part (c) within the context of the fountain’s motion.