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# Use the equation $u t-16 t^{2}=0$, where v=velocity in feet per second and t=time in seconds. A rocket at a fireworks display was launched with the initial velocity of 208 ft/sec. How many seconds was it in the air before it splashed down in the lake?

Solution

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Determine the time for the given equation.

\begin{align*} 208t - 16t^{2} & = 0 && {\text {substitute for the given value}} \\ 16t \left(13 - t \right) & = 0 && {\text {common monomial factor}} \\\\ 16 t & = 0 && {\text {equate each factor with 0}} \\ \dfrac {16t}{16} & = \dfrac {0}{16} && {\text {divide both sides of the equation by 16}} \\ t & = 0 && {\text {represents the launch time}} \\\\ 13 - t & = 0 && {\text {equate each factor with 0}} \\ 13 - t + t & = 0 + t && {\text {addition property of equality}} \\ 13 \text { seconds } & = t && {\text {time the rocket remains in air}} \end{align*}

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