Question

a projectile is thrown so that it's distance above the ground after t seconds is h(t)=-16t^2+660t. after how many seconds does it reach its maximum height

Answer 1

The function is given to be:

`h(t)=-16t^2+660t`

The vertex of the parabola represents the highest (or lowest) point of a parabola. Given the normal form of a quadratic formula:

`f(x)=ax^2+bx+c`

the vertex is calculated to be:

`x=-(b)/(2a)`

From the function of the projectile given, we have:

`\begin{gathered} a=-16 \\ b=660 \end{gathered}`

Therefore, the vertex is:

`t=-(660)/(2*(-16))=(660)/(32)=20.625`

This can be confirmed by graphing the function:

Therefore, the time taken is 20.625 seconds.