SOLUTION: A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long

Question 1062615: A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.
Thank you. I would like to know how to obtain the answer. as well as the correct answer if you please.
I sincerely appreciate your assistance.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) h(t) = -t^2 +3t +10
:
The graph of h(t) is a parabola that curves downward
:
at t = 0, h(t) = 10, I assume this is the height of the platform above the ground
:
The max height of the rocket is determined from the first derivative
:
dh/dt = -2t + 3
:
-2t + 3 = 0
:
t = 3/2 = 1.5 seconds
:
substitute for t in h(t)
:
h(1.5) = -(1.5)^2 +3(1.5) + 10 = 12.25
:
here is a graph of the parabola
:

:
the rocket reaches the platform when
:
x^2 = 3x
:
x = 3
:
to check this, substitute in equation 1)
:
h(3) = -(3^2) +3(3) + 10 = 10
:
**************************************************
the rocket reaches the platform when t = 3 seconds
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