SOLUTION: i need some help on a word problem for quadratics-it goes like this-a model rocket is fired into the air off the top of a building. the following equation models this motion: h=-1

Question 193440: i need some help on a word problem for quadratics-it goes like this-a model rocket is fired into the air off the top of a building. the following equation models this motion: h=-10t+26t+12 where h is the height in meters above the ground and t is the time in seconds since the launch. and now i have to answer the following questions...A. how high is the building? B. how high will the rocket be after 2.5 seconds? C. when will the rocket reach a height of 12 meters? D. how long will it take for the rocket to hit the ground? E. how long will it take to reach its maximum height? F. what is the maximum height the rocket can go?
i was able to figure out B and C but i am having a little bit of trouble figuring out the rest. i do not want answers i just need a little help getting started on the others. thank you sooo much!!!
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
i need some help on a word problem for quadratics-it goes like this-a model rocket is fired into the air off the top of a building. the following equation models this motion: h=-10t+26t+12 where h is the height in meters above the ground and t is the time in seconds since the launch. and now i have to answer the following questions...
A. how high is the building?
The height of the building is 12 meters, the constant in the equation.
Set t = 0 and find h = 12.
- - - - - - - - - -
The exponent is missing in first term of the eqn, it should be
h = -10t^2 + 26t + 12
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B. how high will the rocket be after 2.5 seconds?
h = -10*6.25 + 26*2.5 + 12 at 2.5 seconds
h = -62.5 + 65 + 12
h = 14.5 meters
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C. when will the rocket reach a height of 12 meters?
Sub 12 for h and solve for t
12 = -10t^2 + 26t + 12
-10t^2 + 26t = 0
t = 0 (at launch)
t = 2.6 seconds (on its way down)
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D. how long will it take for the rocket to hit the ground?
Set h = 0 and solve for t
-10t^2 + 26t + 12 = 0
t = 1.3 + 1.7 = 3 seconds
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E. how long will it take to reach its maximum height? F. what is the maximum height the rocket can go?
Looking part C, it passes the 12 meter mark going up and down at t=0 and t=2.6 seconds. The apogee (highest altitude) is the midpoint, or at 1.3 seconds.
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Sub 1.3 for t to find the apogee:
h = -10*1.69 + 26*1.3 + 12
h = 28.9 meters
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i was able to figure out B and C but i am having a little bit of trouble figuring out the rest. i do not want answers i just need a little help getting started on the others
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