Answer
$2.26\;s$
Work Step by Step
Initial upward velocity $v=35\; ft/s$.
Starting height $c=2.5\; ft$.
Ball's height at the ground $h=0$.
The formula is
$h=-16t^2+vt+c$
Substitute all values.
$0=-16t^2+35t+2.5$
Multiply the equation by $-1$.
$16t^2-35t-2.5=0$
Use the quadratic formula $(a=16,b=-35\; and \; c=-2.5)$.
$t=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
Substitute all values.
$t=\frac{35\pm\sqrt{(-35)^2-4(16)(-2.5)}}{2(16)}$
Simplify.
$t=\frac{35\pm37.2}{32}$
$t=2.26$.
