Question

A model rocket is launched with an initial upward velocity of 113 ft/s. The rocket’s height h (in feet) after t seconds is giving by the following. h=113t-16t^2 Find all values of t for which the rockets height is 39 feet. Round your answer(s) to the nearest hundredth.

Answer 1

`\begin{gathered} h=113t-16t^2 \\ h=39ft \\ 39=113t-16t^2 \\ 16t^2-113t+39=0 \\ Use\text{ quadratic formula to find t} \\ (-b\pm√(b^2-4ac))/(2a) \\ a=16 \\ b=-113 \\ c=39 \\ (-(-113)\pm√(-113^2-4*16*39))/(2*16) \\ (113\pm√(12769-2496))/(32) \\ (113\pm√(10273))/(32) \\ (113\pm101.355808911)/(32) \\ (113+101.355808911)/(32)0r\text{ }(113-101.355808911)/(32) \\ (214.355808911)/(32)\text{ or }(11.644191089)/(32) \\ 0.36388097153\text{ or }6.69861902847 \\ t\approx0.36\text{ or 6.70} \end{gathered}`