Answer:
It will take the object 2 seconds to reach the maximum height.
Step-by-step explanation:
The original equation is [tex]h=-14t^2+56t+60[/tex].
The object reaches the maximum height when derivative of [tex]h[/tex] is zero
[tex]\frac{dh}{dt}=0[/tex]
So let us take evaluate the derivative of [tex]h[/tex]
[tex]\frac{dh}{dt} =\frac{d}{dt} (-14t^2+56t+60)=\frac{d}{dt} (-14t^2)+\frac{d}{dt}(56t)+\frac{d}{dt} (60)[/tex]
[tex]=-28t+56[/tex]
this must be equal to 0:
[tex]-28t+56=0[/tex]
[tex]t=\frac{-56}{-28}[/tex]
[tex]\boxed{ t=2}[/tex]
It will take the object 2 seconds to reach the maximum height.
