A student with a third floor dormitory window 32 feet off the
ground tosses a water balloon straight up in the air with an initial velocity
of 16 feet per second. It turns out that the instantaneous velocity of the water balloon is given by
the velocity function v(t) = -32t+16 , where v is measured in feet per
second and t is
measured in seconds.

Let

At what time does the water balloon reach its maximum height?

At what time
does the water balloon land?

Compute the three differences:

What do these differences represent?

What is the total vertical distance traveled by the water balloon from the time it is
tossed until the time it lands?

Total vertical distance =

The graph of the velocity function

What
is the total net signed area bounded by

Total net signed area =

In order to get credit for this problem all answers must be correct.