Question

How is this equation completed? I cannot find any examples in the book.

Answer 1

Answer: Option D

`t_(max) =19\ s`

Explanation:

Note that the projectile height as a function of time is given by the quadratic equation

`h = -12t ^ 2 + 456t`

To find the maximum height of the projectile we must find the maximum value of the quadratic function.

By definition the maximum value of a quadratic equation of the form

`at ^ 2 + bt + c` is located on the vertex of the parabola:

`t_(max)= -(b)/(2a)`

Where
`a <0`

In this case the equation is:
`h = -12t ^ 2 + 456t`

Then

`a=-12\\b=456\\c=0`

So:

`t_(max) = -(456)/(2*(-12))`

`t_(max) =19\ s`