Question

A model rocket is launched with an initial upward velocity of 195 ft/S the Rockets height H (in feet) after T seconds is given by the following. H= 195T -16 T^2 find all values for t for which the Rockets height is 87 feet. Round your answer to the nearest hundredth

Answer 1

The height, H (in ft), is related to time, T (in seconds), by the next equation:

$H=-16T^2+195T$

Substituting with H = 85 ft we get:

$\begin{gathered} 85=-16T^2+195T \\ 0=-16T^2+195T-85 \end{gathered}$

Applying the quadratic formula:

$\begin{gathered} T_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ T_{1,2}=\frac{-195\pm\sqrt[]{195^2-4\cdot(-16)\cdot(-85)}}{2\cdot(-16)} \\ T_{1,2}=\frac{-195\pm\sqrt[]{32585}}{-32} \\ T_1\approx\frac{-195+180.5}{-32}\approx0.45\text{ seconds} \\ T_2\approx\frac{-195-180.5}{-32}\approx11.73\text{ seconds} \end{gathered}$