Math Homework Late

Question

A rocket is launched from a tower. The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation. Using this equation, find the time that the rocket will hit the ground, to the nearest 100th of second.

Answer 1

General equation is

h(t) = -16t^2 + vot + ho where h(t) = height after t seconds and h=height in feet, vo = initial velocity and ho = initial height. To find when it hits the ground, set h(t) =0 and solve for t

0=-16t^2 + vot +ho

or replace t by x and h by y

-16x^2 + vox + yo = 0

use the quadratic formula if it doesn't factor

x = vo/32 + (1/32)sqr(vo^2 +4(16)yo)

plug in the values for vo and yo and solve for x = time in seconds when it hits the ground