Question 596110: 2. Suppose a rocket is shot into the air with an initial speed of 368 feet per second. The height of the rocket (in feet) above the ground after t seconds is given by h = -16t2 + 368t + 144 where t=0 is the launch time.
(a) Will the rocket reach a maximum height or a minimum height? How do you know?
(b) Describe what happens to the height of the rocket over time.
(c) What is the vertex of the graph of h = -16t2 + 368t + 144 ?
(d) After how many seconds will the rocket reach its peak height?
(e) What will the height of the rocket be at its peak?
(f) Recall that you solved -16x2 + 368x + 144 = 0 in part 1(h,i). What will the solutions to -16t2 + 368t + 144 = 0 be?
(g) What do the solutions to the equation -16t2 + 368t + 144 = 0 represent?
(h) Is there a solution to the equation in 2(f) that doesn’t make sense in the context of the rocket problem? If so, explain why the solution does not make sense.
(i) At what time does the rocket hit the ground?
(j) What is the height of the rocket at time t=0? Did the rocket start out at ground level?
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! Mostly a duplicate.
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2. Suppose a rocket is shot into the air with an initial speed of 368 feet per second. The height of the rocket (in feet) above the ground after t seconds is given by h = -16t2 + 368t + 144 where t=0 is the launch time.
(a) Will the rocket reach a maximum height or a minimum height? How do you know?
(b) Describe what happens to the height of the rocket over time.
It goes up, then it goes down.
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(c) What is the vertex of the graph of h = -16t2 + 368t + 144 ?
Done
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(d) After how many seconds will the rocket reach its peak height?
Done. 11.5 seconds.
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(e) What will the height of the rocket be at its peak?
Done. The y of the vertex.
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(f) Recall that you solved -16x2 + 368x + 144 = 0 in part 1(h,i). What will the solutions to -16t2 + 368t + 144 = 0 be?
The time the rocket is at ground level, h = 0
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(g) What do the solutions to the equation -16t2 + 368t + 144 = 0 represent?
See (f)
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(h) Is there a solution to the equation in 2(f) that doesn’t make sense in the context of the rocket problem? If so, explain why the solution does not make sense.
One solution is negative.
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(i) At what time does the rocket hit the ground?
The positive value.
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(j) What is the height of the rocket at time t=0? Did the rocket start out at ground level?
No. h(0) = 144 feet.
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This is not a rocket. Rockets have engines and they accelerate upward (if things go right). This is just something tossed into the air, a projectile.
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