You have the following function for the height respect to the water, Jason has after time t he jumped:
[tex]h(t)=-16t^2-16t+672[/tex]In order to determine the time Jason takes to hit the water, equal h = 0. Thus, you have a quadratic equation and it is necessary to find the zeros of the polynomial:
[tex]0=-16t^2-16t+672[/tex]use the following quadratic formula to find the zeros:
[tex]t=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]where a,b and c are the coefficients of the polynomial:
a = -16
b = -16
c = 672
replace these values into the formula:
[tex]\begin{gathered} t=\frac{-(-16)\pm\sqrt[]{(-16)^2-4(-16)(672)}}{2(-16)} \\ t=\frac{16\pm\sqrt[]{43264}}{-32} \\ t=\frac{16\pm208}{-32} \\ t=-0.5\pm(-6.5) \end{gathered}[/tex]Then, you obtain the following two values:
[tex]\begin{gathered} t=-7 \\ t=6 \end{gathered}[/tex]Select the positive values because negative time does not have physical meaning.
Hence, Jason takes 6 seconds to hit the water.
