From Mechanics

The frisby hits the ground when the \displaystyle \mathbf{k} term is zero.

This gives

\displaystyle \begin{align} & 24+5t-{{t}^{\ 2}}=0 \\ & \\ & {{t}^{\ 2}}-5-24=0 \\ \end{align}

This quadratic equation in \displaystyle t is to be solved. We factorise the equation.

\displaystyle \left( t+3 \right)\left( t-8 \right)=0

giving solutions

\displaystyle t=-3 and \displaystyle t=8

The first solution is mathematically correct, but is of no interest as we are looking for a positive time. We must choose the second solution.

\displaystyle t=8 \text { s}