Given data:
The expression for the height is h=-10t^2 +40t+2.
Equate the derivative of the height to zero in order to mmaximize the height.
[tex]\begin{gathered} \frac{dh}{dt}=0 \\ \frac{d}{dt}(-10t^2+40t+2)=0 \\ -20t+40=0 \\ -20t=-40 \\ t=2 \end{gathered}[/tex]Substitute 2 for t in the given expression of height.
[tex]\begin{gathered} h=-10(2)^2+40(2)+2 \\ =-40+80+2 \\ =42\text{ ft} \end{gathered}[/tex]Thus, the maximum height of the stone is 42 feet.
