Question 182343: Quadratic Function:
If a soldier in basic training fires a rocket propelled grenade straight up from ground level with an initial velocity of 256 ft/sec, then its height above the ground at time t seconds is given by function h(t) = -16t^2 + 256t.
1. What is the maximum height reached by the grenade?
2. How long does it take for the grenade to reach the ground?
Answer by tvandenberg(45)   (Show Source):
You can put this solution on YOUR website! 1. I hope you know derivatives, because the easiest way to solve this is to take the first derivative, and you know at the top it will have a slope of 0, we can solve for the time there, and then substitute that back in to get the height.
h'(t)=-32t+256=0 --> -32t = -256 --> t = 8 (sec)
h(8) = -16(8^2)+256*8 = 1024 (ft)
2. This isn't as hard, we know that it rests at h(t) = 0. Note, this will have two roots, first at t = 0, since the rocket starts from the ground.
h(t) = 0 = -16*t^2 + 256t --> t(-16t+256) = 0
Again, one root is t = 0, other is -16t + 256 = 0
16t = 256 --> t = 16 (sec)
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