Question

A model rocket is launched with an initial upward velocity of . The rocket's height (in meters) after seconds is given by the following.Find all values of for which the rocket's height is meters.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or" button.)

Answer 1

$h=57t-5t^2$

For h = 29:

$\begin{gathered} 29=57t-5t^2 \\ 5t^2-57t+29=0 \end{gathered}$

Solve it using the quadratic equation:

$\begin{gathered} t=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ where: \\ a=5 \\ b=-57 \\ c=29 \\ ------ \\ so: \\ t=\frac{57\pm\sqrt{(-57^2)-4(5)(29)}}{2(5)} \\ t=\frac{57\pm\sqrt{2669}}{10} \\ t=10.87 \\ or \\ t=0.53 \end{gathered}$

Answer:

0.53 or 10.87