SOLUTION: I shot a rocket from the roof of a second story house. The rocket propelled upward with an initial velocity of 44ft/sec and it's height after t seconds is given by
H (t)=-16t2+44
Algebra.Com
Question 971165: I shot a rocket from the roof of a second story house. The rocket propelled upward with an initial velocity of 44ft/sec and it's height after t seconds is given by
H (t)=-16t2+44t
How long will it take to reach its highest point and how high will it go. Assume that each floor of the house requires 12 feet of vertical space
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Your height function is incorrect. The function you provided is the height ABOVE the roof of the house. The correct function is:
\ =\ -16t^2\ +\ v_ot\ +\ h_o)
where 
is the initial velocity and 
is the initial height of the projectile when it was fired. Since each floor of the hous measures 12 feet, one must presume that this value is equal to 24 feet. Your function is therefore:
\ =\ -16t^2\ +\ 44t\ +\ 24)
Algebra method
The height function is a quadratic polynomial that has a graph that is a parabola. Since the lead coefficient is negative, the parabola opens downward and the )
coordinate of the vertex represents the maximum height of the projectile and the 
coordinate of the vertex represents the time at which the projectile reaches that maximum height.
The coordinates of the vertex of
\ =\ ax^2\ +\ bx\ +\ c)
are given by
 = f\left(\frac{-b}{2a}\right))
So for your situation
})
You can do your own arithmetic to find 
Then
\ =\ -16(t_{max})^2\ +\ 44t_{max}\ +\ 24)
Just substitute and calculate.
Calculus Method
The local maximum is the point where the first derivative is equal to zero, so
Set 
And solve for
Then
Just substitute and calculate.
John
My calculator said it, I believe it, that settles it
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