Answer
a) $h = -16t^2+38t+5$
b) 2.5 seconds
Work Step by Step
b)
$h = -16t^2+38t+5$
$0 = -16t^2+38t+5$
$-16t^2+40t-2t+5 = 0$
$-16t(t-2.5)-2(t-2.5) = 0$
$(-16t-2)(t-2.5)=0$
$-16t-2 = 0$
$-16t-2 +16t = 0+16t$
$-2 = 16t$
$-2/16 = 16t/16$
$-1/8 = t$
$t-2.5=0$
$t-2.5 +2.5 = 0+2.5$
$t = 2.5$