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Sagot :
The function that models the height of the plane is:
[tex]h(t)=-16t^2+32t+48[/tex]The plane will hit the ground when the height is zero, this means:
[tex]\begin{gathered} h(t)=0 \\ -16t^2+32t+48=0 \end{gathered}[/tex]hence, we need to solve the equation for t. Let's do this:
[tex]\begin{gathered} -16t^2+32t+48=0 \\ -16(t^2-2t-3)=0 \\ t^2-2t-3=\frac{0}{-16} \\ t^2-2t-3=0 \\ (t-3)(t+1)=0 \\ \text{then} \\ t-3=0 \\ t=3 \\ or \\ t+1=0 \\ t=-1 \end{gathered}[/tex]Therefore the possible values for t are 3 and -1. Since the time has to be positive we conclude that it takes 3 second for the plane to crash.
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