Question

the function h=-16t^2+48t represents the height h (in feet) of a kickball t seconds after it is kicked from the ground

Answer 1

Answer:

36 feet

Step-by-step explanation:

Given

$h(t) = -16t^2 + 48t$

Required

Determine the maximum height attained

First, calculate the time to reach maximum height;

In a quadratic equation;

$y = ax^2 + bx + c$

The maximum is:

$x = -\frac{b}{2a}$

So, we have:

$t = -\frac{b}{2a}$

Where

$a = -16; b = 48$

So:

$t = -\frac{b}{2a}$

$t = -\frac{48}{2 * -16}$

$t = -\frac{48}{-32}$

$t = \frac{48}{32}$

$t = 1.5$

The maximum height is at: $t = 1.5$

So, we have:

$h(t) = -16t^2 + 48t$

$h_{max}=-16 * 1.5^2 + 48 * 1.5$

$h_{max}=36$