Question

A projectile is shot into the air following the path, h(t) = -3t^2 + 12t - 5. At what time, value of t, will it reach a maximum height?

Answer 1

From the question given, the projectile follows the path

`h\mleft(t\mright)=-3t^2+12t-5`

At maximum height

`h^(\prime)(t)=0`

Hence, we will have to find the derivative of the function, and then get the time t.

`\begin{gathered} h\mleft(t\mright)=-3t^2+12t-5 \\ h^(\prime)(t)=-6t+12 \\ \text{But } \\ h^(\prime)(t)=0 \\ \text{Then } \\ -6t+12=0 \\ 6t=12 \\ t=(12)/(6) \\ t=2 \end{gathered}`

Hence the answer is t = 2