this is the work that I used, however, I'm not sure that this is the correct approach. At a particular time, the sandbag goes from an upward acceleration of g/4 to free fall.
I got to the quadratic equation of the motion where: 4gt^(2) - g(delta t)t - g(delta t) = 0 and tried to solve for t. In this case, we would take the positive discriminate since we are dealing with the passing of time.
t = ((sqrt(17) g(delta t)) + g (delta t)) / (8g)
However, this is the...