Answer
The maximum height of the baseball is 51.0 feet.
The ball has traveled a horizontal distance of 55.36 feet.
Work Step by Step
$y = 55.4~t-16~t^2+3$
$y = -16~t^2+55.4~t+3$
When $y = at^2+bt+c$, the vertex of the parabola is at the point $t=-\frac{b}{2a}$
We can find $t$ of the vertex:
$t=-\frac{b}{2a}$
$t=-\frac{55.4}{(2)(-16)}$
$t = 1.73$
We can find the height when $t = 1.73$:
$y = 55.4~t-16~t^2+3$
$y = (55.4)(1.73)-(16)(1.73)^2+3$
$y = 51.0~feet$
The maximum height of the baseball is 51.0 feet.
We can find the horizontal distance at $t = 1.73$:
$x = 32~t$
$x = (32)(1.73)$
$x = 55.36~feet$
The ball has traveled a horizontal distance of 55.36 feet.
