A hot-air 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?

Answer 1

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