Question

To celebrate July 4th, fireworks ate Lau cheddar over a lake from a dam 36 ft above the water. The height of a display. t seconds after it has been launched, is given by h(t)=-16t^2+64t+36

Answer 1

Given

$h(t)=-16t^2+64t+36$

Find

How long will it take for a "dud" firework to reach the water?

Explanation

When dud reach the water the height becomes zero

The height of a display, t seconds after it has been launched, is given by

$\begin{gathered} -16t^2+64t+36=0 \\ 4(-4t^2+16t+9)=0 \\ -4t^2+16t+9=0 \\ -4t^2+18t-2t+9=0 \\ -2t(2t-9)-1(2t-9)=0 \\ (-2t-1)(2t-9)=0 \\ 2t-9=0 \\ t=\frac{9}{2}=4.5\text{ }seconds \end{gathered}$

Final Answer

Hence , the time will it take for a dud firework to reach the water is 4.5 seconds.