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A model rocket flies up into the sky. When the rocket reaches a height of 500500 feet, it starts to fall back down. The rocket's height above the ground in feet can be modeled by the expression 50016t2500 - 16t^2, where tt is the time in seconds after the rocket starts to fall back down.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the rocket to fall tt feet\newline(B)the time in seconds it takes for the rocket to reach a height of tt feet\newline(C)the height in feet of the rocket above the ground after tt seconds\newline(D)the distance in feet the rocket has fallen after tt seconds\newline

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Q. A model rocket flies up into the sky. When the rocket reaches a height of 500500 feet, it starts to fall back down. The rocket's height above the ground in feet can be modeled by the expression 50016t2500 - 16t^2, where tt is the time in seconds after the rocket starts to fall back down.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the rocket to fall tt feet\newline(B)the time in seconds it takes for the rocket to reach a height of tt feet\newline(C)the height in feet of the rocket above the ground after tt seconds\newline(D)the distance in feet the rocket has fallen after tt seconds\newline
  1. Initial Height Explanation: The expression for the rocket's height is 50016t2500 - 16t^2. We know that 500500 is the initial height, so 16t216t^2 must be related to the change in height over time.
  2. Height Decrease Over Time: Since the rocket is falling, the height decreases over time. The term 16t2-16t^2 indicates that the height is being reduced by some factor of time squared.
  3. Acceleration Due to Gravity: The number 1616 in the term 16t216t^2 is a constant that relates to the acceleration due to gravity, which is approximately 3232 feet per second squared. Since the formula is 50016t2500 - 16t^2, it means we're taking half of the acceleration due to gravity, which is typical for free-falling objects in a quadratic equation.
  4. Distance Fallen Representation: Therefore, 16t216t^2 represents the distance in feet that the rocket has fallen after tt seconds, because it's the part of the expression that changes with time.

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