SOLUTION: A toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second. The height, h is given by the equation h(t)=-16t^2+128t (without any a
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-> SOLUTION: A toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second. The height, h is given by the equation h(t)=-16t^2+128t (without any a
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Question 970087: A toy rocket is launched vertically upward from ground level with an initial velocity of 128 feet per second. The height, h is given by the equation h(t)=-16t^2+128t (without any air resistance)
How long will it take for the rocket to reach its maximum height?
What is the maximum height of the rocket?
How long will it take for the rocket to return to the ground?
After how many seconds will the rocket be 112 feet above the ground?
Why is the equation including h(t)= rather then y=? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! h(t)=-16t^2+128t
maximum height occurs at the vertex.
t value at vertex is -b/2a
b=128
a=-16
vertex has t value of -128/-32 = 4 seconds to reach maximum height
h(4)=-16 (4^2) + (128) (4)
h=-256+512=256feet
4 seconds to return to ground, because launched from ground, and parabolas are symmetric.
112=-16(t^2) +128
Divide everything by 16
7=-1 (t^2) +8
-1=-1 (t^2)
1=1 t^2
t^2=1
t=(1) second OR 7 seconds, on the way down. Note, t=-1 is a mathematical but not real world solution.
It is h(t), because height is a function of t. That is by convention.
