A rocket is fired upward from some initial distance above the ground. It's height in feet, h, above the ground, t seconds after it is fired is give by h=-16t^2+48t+4864. What is the rockets maximum height? How long does it take the rocket to reach it's maximum height? After it is fired, the rocket reaches the ground at t= __sec.

Question

anonymous · Answer

do you know calculus?

anonymous · Answer

derivative to be specific

anonymous · Answer

not at all, just taking a test at the moment.

anonymous · Answer

Oh ok, then do you know how to find vertex of a parabola?

anonymous · Answer

i honestly know nothing...haha

anonymous · Answer

y = ax^2 + bx + c
equation for vertex = 
$$\frac{ -b }{ 2a }$$
In this case, a = -16 and b = 48
Plug it in the equation to find vertex
The vertex of a downward parabola gives you the maximum height of the rocket.

anonymous · Answer

vertex = time of maximum height.
48/-(-16)
= 3 seconds

anonymous · Answer

maximum height = -16(3)^2 + 48(3) + 4864

anonymous · Answer

so maximum height is 4864? & after it is fired how many secs till it reaches the ground?

anonymous · Answer

then to find when it reaches the groung again, set h = 0 then solve for the equation
0= -16t^2 + 48t + 4864
0= -16(t^2 - 3t - 304) 
0 = -16(t-19)(t+16)
t= 19, -16, 
since t cannot be negative, the only answer is 19 seconds for time on the ground

anonymous · Answer

I gave you the equation for maximum height.  it's not 4864

anonymous · Answer

my time already ran up, but thank you away! :)