Question 181576: If a soldier in basic training fores a rocket propelled grenade straight up from the ground level with an initial velocity of 256 ft/sec, then its height above the ground at time t seconds is given by the function h(t) = -16t^2 + 256t.
A. what is the maximum height reached by the grenade?
B. How long does it take for the grenade to reach the ground?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! If a soldier in basic training fores a rocket propelled grenade straight up from the ground level with an initial velocity of 256 ft/sec, then its height above the ground at time t seconds is given by the function h(t) = -16t^2 + 256t.
A. what is the maximum height reached by the grenade?
B. How long does it take for the grenade to reach the ground?
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1st of all, an RPG has a rocket motor, it will accelerate straight up. RP means Rocket Propelled.
This problem would apply to a short range mortar, or, with the numbers given, a hand grenade.
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Anyway,
For max height, find where the time when the upward speed is zero, which is where it stops going up and starts going down.
To do that, set the 1st derivative to zero.
-32t + 256 = 0
t = 8 seconds.
At t=8, the height is 256*8 - 16*64
A. hmax = 1024 feet (optimistic for a hand grenade)
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B. It takes the same time to fall as it does to reach max height, so that's 16 seconds.
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