An improvised rocket is launched from the top of a building 150 feet high. The height (H) reached by the rocket after (t) seconds is given by the function:
H(t) = 40t - 10t^2.
How long does it take for the rocket to reach an altitude of 180 feet.
If the formula for height from the top of a building 150 feet high is: H(t) = 40t - 10t2,
then the formula for height from the ground is: H*(t) = 40t - 10t2 + 150.
Solving H* to find the length of time it takes to reach an altitude of 180 feet:
H*(t) = 180 ---> 40t - 10t2 + 150 = 180
-10t2 + 40t - 30 = 0
dividing by -10: t2 - 4t + 3 = 0
factoring: (t - 3)(t - 1) = 0
solving: either t = 3 or t = 1
It will take 1 second for the rocket to reach an altitude of 180 feet.
At 3 seconds, it will again be at 180 feet, only this is when it is coming down.