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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.

 Jun 22, 2020
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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.

 Jun 22, 2020

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