A rocket is launch from the top of an 40 foot cliff with an initial velocity of 140 feet per second, the height h of the rocket after t seconds is given by the equation h=16t^2+140t+40. How long after the rocket is launch will be 30 feet from the ground?

Answer 1

First of all the equation should say:

h = -16t^2 + 140t + 40

you want h = 30
30 = -16t^2 + 140t + 40
16t^2 - 140t - 10 = 0

t = (140 ± √20240)/32
= 8.8 or a negative, which we will reject

it would take about 8.8 seconds to reach a height of 30 ft (on its way down)