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A small toy rocket is launched from a 12-foot pad. The height (h, in feet) of the rocket t seconds after taking off is given by the formulah=−2tcubed2−2+12How long will it take the rocket to hit the ground?t= (Separate answers by a comma if applicable. Write answers as integers or reduced fractions.)

A small toy rocket is launched from a 12foot pad The height h in feet of the rocket t seconds after taking off is given by the formulah2tcubed2212How long will class=

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Solution

Gievn:

[tex]h=-2t^2-2t+12[/tex]

When the rocket hits the ground. The distance is zero

Set h = 0 and solve for t

[tex]\begin{gathered} -2t^2-2t+12=0 \\ 2t^2+2t-12=0 \\ 2t^2+6t-4t-12=0 \\ 2t(t+3)-4(t+3)=0 \\ (t+3)(2t-4)=0 \end{gathered}[/tex][tex]\begin{gathered} t+3=0\text{ or 2t-4=0} \\ t=-3\text{ or 2t=4} \\ t=-3\text{ or t=}\frac{4}{2}=2 \end{gathered}[/tex]

But, time can not be in negative, hence the answer t = 2

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