Question 192759
the height h of a toy rocket t seconds after launching is determined by the formula h= -16t^2 + 112t
a)find the height of the rocket 2.5 seconds after launching
h(2.5) = -16(2.5)^2 + 112(2.5) = 180 ft.
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b) afer how many seconds is the rocket 196 feet above the ground?
-16t^2 + 112t = 196
-16t^2 + 112t - 196 = 0
t^2 - 7t + 12.25 = 0
t = [7 +- sqrt(49 - 4*1*+12.25)]/2
t = [7 +- sqrt(49 - 49)]/2
t = [7 +- sqrt(0)]/2
Positive solution:
t = 7/2 = 3.5 seconds

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c) when will the rocket hit the ground?
-16t^2 + 112t = 0
-16t(t - 7) = 0
t = 0 (means it starts on the ground)
t = 7 sec (means it ends up on the ground in 7 seconds)
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Cheers,
Stan H.