SOLUTION: A model rocket is launched from the roof of a building. Its flight path is modeled by h equals minus 5 t squared plus 30 t plus 10 where h is the height of the rocket above the gr

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A model rocket is launched from the roof of a building. Its flight path is modeled by h equals minus 5 t squared plus 30 t plus 10 where h is the height of the rocket above the gr      Log On


   

Question 864627: A model rocket is launched from the roof of a building. Its flight path is modeled by h equals minus 5 t squared plus 30 t plus 10 where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.
What is the rocket's maximum height?
How long before the rocket reaches the ground?
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
A model rocket is launched from the roof of a building. Its flight path is modeled by h equals minus 5 t squared plus 30 t plus 10 where h is the height of the rocket above the ground in meters and t is the time after the launch in seconds.
What is the rocket's maximum height?
How long before the rocket reaches the ground?
***
h=-5t^2+30t+10
complete the square:
h=-5(t-6+9)+45+10
h=-5(t-3)^2+55
This is an equation of a parabola that opens down with vertex at (3,55)
maximum height=55m
..
when rocket reaches the ground, h=0
-5t^2+30t+10=0
5t^2-30t-10=0
solve by quadratic formula:
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=5, b=-30, c=-10
ans: t≈6.32 sec
maximum height? 55m
How long before the rocket reaches the ground? 6.32sec