Answer
The velocity is $-118$ feet per second after three seconds.
The velocity is $-86$ feet per second after falling 108 feet.
Work Step by Step
$s(t)=-16t^2+v_0t+s_0$
$\frac{d}{dt}s(t)=v$
$\frac{d}{dt}s(t)=-32t+v_0$
$v=-32t+v_0$
$v_0=-22$
$v=-32t-22$
After three seconds $(t=3)$, the velocity is:
$v=-32(3)-22$
$v=-118$ feet per second
When the ball falls 108 feet from a 220-foot building, its 112 feet above the ground.
$s_0=220$
$s(t)=112$
$s(t)=-16t^2+v_0t+s_0$
$112=-16t^2+(-22)t+220$
$-16t^2-22t+108=0$
$-8t^2-11t+54=0$
$(2-t)(8t+27)=0$
$t=2$ or $-27/8$
$t$ can't be negative.
$t=2$.
The ball falls 108 feet after 2 seconds.
$v=-32t-22$
$v=-32(2)-22$
$v=-86$ feet per second
