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An earthquake dislodges a rock from the side of a cliff, and the rock falls to the ground below. The rock's height above the ground in meters can be modeled by the expression 50−4.9t250 - 4.9t^2, where tt is the time in seconds after the rock starts to fall.\newlineWhat does the quantity 4.9t24.9t^2 represent in the expression?\newlineChoices:\newline(A)the height in meters of the rock above the ground after tt seconds\newline(B)the distance in meters the rock has fallen after tt seconds\newline(C)the time in seconds it takes for the rock to fall tt meters\newline(D)the time in seconds it takes for the rock to reach a height of tt meters\newline

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Q. An earthquake dislodges a rock from the side of a cliff, and the rock falls to the ground below. The rock's height above the ground in meters can be modeled by the expression 50−4.9t250 - 4.9t^2, where tt is the time in seconds after the rock starts to fall.\newlineWhat does the quantity 4.9t24.9t^2 represent in the expression?\newlineChoices:\newline(A)the height in meters of the rock above the ground after tt seconds\newline(B)the distance in meters the rock has fallen after tt seconds\newline(C)the time in seconds it takes for the rock to fall tt meters\newline(D)the time in seconds it takes for the rock to reach a height of tt meters\newline
  1. Initial Height Explanation: The expression for the rock's height is 50−4.9t250 - 4.9t^2. Since the rock starts at a height of 5050 meters, the term 5050 represents the initial height.
  2. Distance Fallen Representation: The term 4.9t24.9t^2 must represent the distance the rock has fallen after tt seconds, because it's being subtracted from the initial height to give the current height.
  3. Gravity Acceleration Relation: Gravity on Earth accelerates objects at approximately 9.89.8 meters per second squared. The term 4.94.9 is half of 9.89.8, which indicates that the expression accounts for the acceleration due to gravity.
  4. Time Dependency Explanation: Since 4.9t24.9t^2 is the part of the expression that changes with time, it cannot represent a constant height (AA) or a specific time (CC or DD). It must represent the distance fallen, which changes as time squared due to acceleration from gravity.

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