Answer
a) 284 feet
b) 536 feet
c) 756 feet
d) 944 feet
e) Eventually, the rocket must hit ground (and return to a height of 0 feet). Also, eventually, $abs(-16t^2) > abs(300t)$.
f) 19 seconds
Work Step by Step
$P(t)=-16t^2+300t$
a)
$t=1$
$P(t)=-16t^2+300t$
$P(1)=-16*1^2+300*1$
$P(1)=-16+300$
$P(1)=284$
b)
$t=2$
$P(t)=-16t^2+300t$
$P(2)=-16*2^2+300*2$
$P(2)=-64+600$
$P(2)=536$
c)
$t=3$
$P(t)=-16t^2+300t$
$P(3)=-16*3^2+300*3$
$P(3)=-144+900$
$P(3)=756$
d)
$t=4$
$P(t)=-16t^2+300t$
$P(4)=-16*4^2+300*4$
$P(4)=-16*16+1200$
$P(4)=-256+1200$
$P(4)=944$
f)
$P(t)=-16t^2+300t$
$-16t^2+300t$
$4t(-4t+75)$
$4t=0$
$4t/4=0/4$
$t=0$
$-4t+75=0$
$75=4t$
$75/4=4t/4$
$75/4=t$
$75/4 = 18.75$
