Answer
a) 20 feet
b) $t= (15 + \sqrt {321})/16$ seconds, 2.1 seconds
Work Step by Step
a)
$d(t)=-16t^2+30t+6$
$d(1)=-16*1^2+30*1+6$
$d(1)=-16*1+30+6$
$d(1)=-16+36$
$d(1)=20$
b)
$d(t)=-16t^2+30t+6$
$0=-16t^2+30t+6$
$-16t^2+30t+6=0$
$-16t^2+30t+6-6=0-6$
$-16t^2+30t=-6$
$-16(t^2-30/16t)=-6$
$-16(t^2-15/8t)=-6$
$-16(t^2-15/8t+(-15/8*1/2)^2=-6+(-16)(-15/8*1/2)^2$
$-16(t^2-15/8t+(-15/16)^2)= -6+(-16)(-15/16)^2$
$-16(t^2-15/8t+(225/256)) = -6+(-16)(225/256) $
$-16(t^2-15/8t+225/256) = -6+(-225/16) $
$-16(t-15/16)^2 = -96/16-225/16$
$-16(t-15/16)^2 = -321/16$
$-1/16*-16(t-15/16)^2 =-1/16*-321/16$
$(t-15/16)^2=321/256$
$\sqrt {(t-15/16)^2}=\sqrt {321/256}$
$t-15/16 = \sqrt {321} /16$
We want time, so we don’t want the negative square root.
$t-15/16 = \sqrt {321} /16$
$t-15/16+15/16 =15/16+\sqrt {321} /16$
$t= (15 + \sqrt {321})/16$
$t=(15+17.916)/16$
$t= 32.916/16$
$t = 2.06$
