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

SOLUTION

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.

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

Hence the answer is t = 2