physics
posted by ray .
A hotair balloon is rising upward with a constant speed of 3.06 m/s. When the balloon is 9.31 m above the ground, the balloonist accidentally drops a compass over the side of the balloon. How much time elapses before the compass hits the ground?

Solve this equation for t:
height = 0 = 9.31 + 3.06 t  (g/2) t^2
=  4.9 t^2 + 3.06 t + 9.31
There will be two answers since this is a quadratic equation. Take the positive one.
t = (1/9.8)[3.06  sqrt[(3.06)^2 + 182.5)]
= 1.726 s