Question

A model rocket is launched with an initial upward velocity of 215 fts. The rocket's height à (in feet) after & seconds is given by the followingA =2159-16?Find all values of ? for which the rocket's height is 97 feet.Round your answer(s) to the nearest hundredth.(If there is more than one answer, use the "or* button.)

Answer 1

The height (h) of the rocket is modelled with respect to time (t) as,

$h=215t-16t^2$

Given the instant when height is 97 feet, it is asked to determine the corresponding values of time,

$\begin{gathered} h=97 \\ 215t-16t^2=97 \\ 16t^2-215t+97=0 \end{gathered}$

Solve the above quadratic equation using the quadratic formula,

$\begin{gathered} t=\frac{-(-215)\pm\sqrt[]{(-215)^2-4(16)(97)}}{2(16)} \\ t=\frac{215\pm\sqrt[]{46225^{}-6208}}{32} \\ t=\frac{215\pm\sqrt[]{40017}}{32} \\ t=\frac{215+\sqrt[]{40017}}{32}\text{, }\frac{215-\sqrt[]{40017}}{32} \\ t=12.97,0.47 \end{gathered}$

Thus, the corresponding time instants are 12.97 seconds and 0.47 seconds.