Question

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

Answer 1

Answer: Option D

$t_{max} =19\ s$

Step-by-step 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:

$t_{max}= -\frac{b}{2a}$

Where $a <0$

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

Then

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

So:

$t_{max} = -\frac{456}{2*(-12)}$

$t_{max} =19\ s$