Answer
2.9 seconds
Work Step by Step
$h=-16t^2+12t+200$
height of 100 feet
$h=-16t^2+12t+200$
$100=-16t^2+12t+200$
$0=-16t^2+12t+100$
$0/-4=(-16t^2+12t+100)/-4$
$0=4t^2-3t-25$
We are talking about time, and we can't have negative time, so we want the positive square root.
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-(-3)±\sqrt {(-3)^2-4*4*-25})/2*4$
$x=(3±\sqrt {9+400})/8$
$x=(3±\sqrt {409}/8$
$x=(3±20.22)/8$
This is where we can have a negative square root, but we are talking about time, and we can't have negative time.
$x=(3+20.22)/8$
$x=23.22/8$
$x=2.9025$
