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A pebble is dropped from the edge of a tall cliff into the ocean. The pebble's height above the ocean in feet can be modeled by the expression 400−16t2400 - 16t^2, where tt is the time in seconds after the pebble is released.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the height in feet of the pebble above the ocean after tt seconds\newline(B)the distance in feet the pebble has fallen after tt seconds\newline(C)the time in seconds it takes for the pebble to fall tt feet\newline(D)the time in seconds it takes for the pebble to reach a height of tt feet\newline

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Q. A pebble is dropped from the edge of a tall cliff into the ocean. The pebble's height above the ocean in feet can be modeled by the expression 400−16t2400 - 16t^2, where tt is the time in seconds after the pebble is released.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the height in feet of the pebble above the ocean after tt seconds\newline(B)the distance in feet the pebble has fallen after tt seconds\newline(C)the time in seconds it takes for the pebble to fall tt feet\newline(D)the time in seconds it takes for the pebble to reach a height of tt feet\newline
  1. Initial Height Explanation: The expression for the pebble's height is 400−16t2400 - 16t^2. The 400400 represents the initial height of the pebble above the ocean.
  2. Distance Fallen Calculation: The term 16t216t^2 is subtracted from 400400, which suggests it represents the distance the pebble has fallen after tt seconds, due to gravity.
  3. Acceleration Due to Gravity: Gravity causes objects to accelerate downwards, so the distance fallen over time is related to the acceleration due to gravity, which is 3232 feet per second squared. The term 16t216t^2 is half of this acceleration, indicating it's part of the formula for distance fallen under gravity: d=12⋅g⋅t2d = \frac{1}{2} \cdot g \cdot t^2.
  4. Verification of Term: Since 1616 is half of 3232, the term 16t216t^2 correctly represents the distance fallen due to gravity after tt seconds. This matches choice (B).

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