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A model rocket is launched into the air from ground level. The height in feet is modeled by the function (p(t) = -16t^2 + 32t). Which of the following statements are true? There may be more than one correct response.

A. -16t^2 represents gravity
B. There is no height listed in the equation because the rocket starts on the ground.
C. 32t represents gravity
D. 32t represents the velocity

User Mazel Tov
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1 Answer

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Final answer:

The terms -16t^2 and 32t in the model rocket equation represent the effects of gravity and initial velocity, respectively. Thus, statements -16t^2 represents gravity and there is no height listed because the rocket starts on the ground are true. The term 32t represents the initial velocity, not gravity.

Step-by-step explanation:

The height of a model rocket launched from ground level is modeled by the function p(t) = -16t^2 + 32t. Among the provided statements, -16t2 represents gravity is true because it corresponds to the downward acceleration due to gravity of 32 feet per second square, which is doubled to -16 in the equation to represent the deceleration effect of gravity (the negative sign indicates that gravity is pulling the rocket down). The statement that there is no height listed in the equation because the rocket starts on the ground is also true. On the other hand, the 32t term does not represent gravity; instead, it represents the initial velocity of the rocket (32 feet per second), with the 't' representing time. Therefore, statements A and B are true, while C is false, and D is true in the context that it represents the initial velocity, not continuous velocity.

User Pee
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