Question

A model rocket is launched with an initial upward velocity of 140 fts. The rocket's height h (in feet) after t seconds is given by the following.h=140t -16t^2Find all values of t for which the rocket's height is 68 feet.Round your answer(s) to the nearest hundredth(If there is more than one answer, use the "or" button.)

Answer 1

8.23secs and 0.53secs

Step-by-step explanation:

Given the expression for calculating the height reached by a rocket as;

`h=140t-16t^2`

If the rocket's height is 68feet, then;

`\begin{gathered} 68=140t-16t^2 \\ 16t^2-140t+68=0 \\ 4t^2-35t+17=0 \end{gathered}`

Factorize;

`\begin{gathered} t=\frac{-(-35)\pm\sqrt[]{(-35)^2-4(4)(17)}}{2(4)} \\ t=\frac{35\pm\sqrt[]{1225-272}}{8} \\ t=\frac{35\pm\sqrt[]{953}}{8} \\ t=(35\pm30.8)/(8) \\ t=(35+30.8)/(8)or(35-30.8)/(8) \\ t=(65.8)/(8)or(4.2)/(8) \\ t=8.23or0.53 \end{gathered}`

Hence the required values of t are 8.23secs and 0.53secs