Activity 1.5.4.
A water balloon is tossed vertically from a window at an initial height of 37 feet and with an initial velocity of 41 feet per second.
(a)
Determine a formula, \(s(t)\text{,}\) for the function that models the height of the water balloon at time \(t\text{.}\)
(b)
Plot the function in Desmos in an appropriate window. Sketch a copy of the graph here.
(c)
Use the graph to estimate the time the water balloon lands.
(d)
Use algebra to find the exact time the water balloon lands.
(e)
Determine the exact time the water balloon reaches its highest point and its height at that time.
(f)
Compute the average rate of change of \(s\) on the intervals \([1.5, 2]\text{,}\) \([2, 2.5]\text{,}\) \([2.5,3]\text{.}\) Include units on your answers and write one sentence to explain the meaning of the values you found. Sketch appropriate lines on the graph of \(s\) whose respective slopes are the values of these average rates of change.
