A ball is thrown from initial height of 2 feet with an initial upward velocity of 35 ft./s. The ball's height H (in feet) after T seconds is given by the following. H=2+35T-16T^2 Find all values of T for which the ball's height is 20 feet. Round your answer(s) to the nearest hundredth.

QUESTION POSTED AT 01/06/2020 - 04:33 PM

Answered by admin AT 01/06/2020 - 04:33 PM

So if the height is going to be 20ft, that means 20 = 2+35t-16t²

\bf 20=2+35t-16t^2\implies 16t^2-35t+18=0
\\\\\\
\textit{now, it doesn't factor in integers, thus}
\\\\\\
 \textit{quadratic formula}\\\\
x= \cfrac{ - {{ b}} \pm \sqrt { {{ b}}^2 -4{{ a}}{{ c}}}}{2{{ a}}}\implies t=\cfrac{-(-35)\pm\sqrt{(-35)^2-4(16)(18)}}{2(16)}
\\\\\\
t=\cfrac{35\pm\sqrt{73}}{32}\implies t\approx
\begin{cases}
1.361\\
0.828
\end{cases}
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