Answer:
14 s
Step-by-step explanation:
We notice that the expression that shows the distance above ground as a function of time, is in fact a quadratic expression (parabola) with negative leading coefficient (-16). this means that the graph of the projectile's distance from the ground is a parabola with branches pointing down, and therefore must have a maximum value at its vertex.
We can then used the formula for finding the horizontal position of the vertex in a quadratic function of the general form [tex]y=ax^2+bx+c[/tex]:
[tex]x_{vertex}=-\frac{b}{2a}[/tex]
In our polynomial [tex]h=-16\,t^2+440\,t[/tex], the horizontal variable is the time (t), the value of [tex]a[/tex] is "-16", and [tex]b[/tex] is "440". Therefore, the time (horizontal variable) at which the projectile reaches the maximum height is:
[tex]t_{vertex}=-\frac{440}{2\,(-16)} \\t_{vertex}=\frac{-440}{-32} \\t_{vertex}=13.75 \,seconds[/tex]
So we can round this answer to the nearest integer giving us about 14 seconds.
