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A coconut falls from the top of a tall palm tree. The coconut's height above the ground in feet can be modeled by the expression 5016t250 - 16t^2, where tt is the time in seconds after the coconut begins to fall.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the coconut to fall tt feet\newline(B)the time in seconds it takes for the coconut to reach a height of tt feet\newline(C)the distance in feet the coconut has fallen after tt seconds\newline(D)the height in feet of the coconut above the ground after tt seconds\newline

Full solution

Q. A coconut falls from the top of a tall palm tree. The coconut's height above the ground in feet can be modeled by the expression 5016t250 - 16t^2, where tt is the time in seconds after the coconut begins to fall.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the coconut to fall tt feet\newline(B)the time in seconds it takes for the coconut to reach a height of tt feet\newline(C)the distance in feet the coconut has fallen after tt seconds\newline(D)the height in feet of the coconut above the ground after tt seconds\newline
  1. Height Expression Explanation: The expression for the coconut's height is 5016t250 - 16t^2. We know that the initial height is 5050 feet, so the term 16t2-16t^2 must represent the change in height over time.
  2. Acceleration Due to Gravity: The term 16t216t^2 is associated with the acceleration due to gravity, which is 3232 feet per second squared, divided by 22. This is because the formula for the distance fallen under gravity is (1/2)gt2(1/2)gt^2, where gg is the acceleration due to gravity.
  3. Interpretation of 16t216t^2: So, 16t216t^2 is half of 32t232t^2, which means it represents the distance the coconut has fallen after tt seconds, not the time it takes to fall or the height above the ground after tt seconds.

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