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the hight h of a rocket t secs. After the launch when will the rocket reach the hight of 230 feet? when will the rocket be back on the ground

given the equation h=144t-16t2
h=hight
t=seconds
When will the rocket reach the height of 230 feet?
When will the rocket be back on the ground?

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Muhammad C. | Muhammad the grand math tutorMuhammad the grand math tutor
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h = 144t - 16t^2
 
h = 230
 
230 = 144t - 16t^2
 
-230 + 144t - 16t^2 = 0
 
16t^2 -144t + 230 = 0
 
8t^2 - 72t + 115 = 0
 
t = (72 +/- (5084 - 3680)^.5)/16 =(72 +/- 6(39)^.5)/16 = 4.5 +/- (3/8)(39)^.5 = 6.84 seconds & 2.16 seconds
 
At these two times, the rocket is at a height 230 feet above the ground.
 
144t - 16t^2 = 0
 
t(144 - 16t) = 0
 
144 - 16t = 0
 
t = 9
 
At 9 seconds, the rocket comes back to the ground.