Answer
a) 0 seconds: 960 feet; 3 seconds: 1008 feet; 6 seconds: 768 feet; 9 seconds: 240 feet
b) Eventually, $abs(-16t^2) > abs(64t+960)$, so the object will hit the ground.
c) $-16(t-10)(t+6)$
Work Step by Step
$h(t)=-16t^2+64t+960$
a)
$t=0$
$h(t)=-16t^2+64t+960$
$h(0)=-16*0^2+64*0+960$
$h(0)=-16*0+64*0+960$
$h(0)=960$
$t=3$
$h(t)=-16t^2+64t+960$
$h(3)=-16*3^2+64*3+960$
$h(3)=-16*9+192+960$
$h(3)=-144+1152$
$h(3)= 1008$
$t=6$
$h(t)=-16t^2+64t+960$
$h(6)=-16*6^2+64*6+960$
$h(6)=-16*36+384+960$
$h(6)=-576+1344$
$h(6)=768$
$t=9$
$h(t)=-16t^2+64t+960$
$h(9)=-16*9^2+64*9+960$
$h(9)=-16*81+576+960$
$h(9)=-1296+1536$
$h(9)=240$
c)
$h(t)=-16t^2+64t+960$
$-16t^2+64t+960$
$-16(t^2-4t-60)$
$-16(t-10)(t+6)$