Question 141673: A model rocket is shot straight up from the roof of a school. The height at any time t is approximated by the model H=15 + 23t - 5t^2,where H is the height in metres and t is the time in seconds.
a)how long does it take for the rocket to pass a window 10 m above the ground.
b) when does the rocket hit the ground?
c) what is the maximum height the rocket reaches above the roof of the school?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A model rocket is shot straight up from the roof of a school. The height at any time t is approximated by the model H=15 + 23t - 5t^2,where H is the height in metres and t is the time in seconds.
a)how long does it take for the rocket to pass a window 10 m above the ground.
-5t^2+23t+15 = 10
-5t^2+23t+5 = 0
t = [-23 +- sqrt(23^2-4*-5*5)]/(-10)
t = [-23 +- sqrt(629)
t = [-23-25.07987..]/(-10)
t = -48.07987]/(-10)
t = 4.80798 seconds
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Comment: The rocket is at 15 meters when it is launched.
It arrives at a height of 10 m after 4.80798 seconds on
its way down to the ground.
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b) when does the rocket hit the ground?
-5t^2+23t+15 = 0
t = [-23 +- sqrt(23^2-4*-1*15)]/(-10)
t = [-23 +- sqrt(829)]/(-10)
t = [-23 +- 28.7924..]/(-10)
t = 5.17924 seconds
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c) what is the maximum height the rocket reaches above the roof of the school?
Max occurs when t = -b/2a = -23/(-10) = 2.3 seconds
H(t) =15 + 23t - 5t^2
H(2.3) = 15 + 23*2.3 - 5(2.3)^2
H(2.3) = 41.45 m
That is 41.45 - 15 = 26.45 m above the root of the school.
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Cheers,
Stan H.
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