There is a straight form of solving this problem by using the formula
, (F_F 4),
which it can be solved for the time when the initial velocity and final
position of the balloon are known.
In order for solving for the time in the previous
equation, it is necessary to solve the following quadratic equation,
from where the time is
As all quadratic equations, two mathematical
solutions have been obtained each of them corresponding to the possible
different signs. By understanding the actual physical situation, the
actual solution to the problem can be recognized.