Question

A projectile is thrown upward so that its distance above the ground after t seconds is h = -16t2 + 440t.

Answer 1

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 $y=ax^2+bx+c$:

$x_{vertex}=-\frac{b}{2a}$

In our polynomial $h=-16\,t^2+440\,t$, the horizontal variable is the time (t), the value of $a$ is "-16", and $b$ is "440". Therefore, the time (horizontal variable) at which the projectile reaches the maximum height is:

$t_{vertex}=-\frac{440}{2\,(-16)} \\t_{vertex}=\frac{-440}{-32} \\t_{vertex}=13.75 \,seconds$

So we can round this answer to the nearest integer giving us about 14 seconds.