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.

Guest Jun 22, 2020

#1**0 **

If the formula for height from the top of a building 150 feet high is: H(t) = 40t - 10t^{2},

then the formula for height from the ground is: H*(t) = 40t - 10t^{2} + 150.

Solving H* to find the length of time it takes to reach an altitude of 180 feet:

H*(t) = 180 ---> 40t - 10t^{2} + 150 = 180

-10t^{2} + 40t - 30 = 0

dividing by -10: t^{2} - 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.

geno3141 Jun 22, 2020