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A piece of ice falls off the side of a glacier and into the ocean. Its height above the ocean in meters can be modeled by the expression 334.9t233 - 4.9t^2, where tt is the time in seconds after the piece of ice begins to fall.\newlineWhat does the quantity 4.9t24.9t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the piece of ice to reach a height of tt meters\newline(B)the distance in meters the piece of ice has fallen after tt seconds\newline(C)the time in seconds it takes for the piece of ice to fall tt meters\newline(D)the height in meters of the piece of ice above the ocean after tt seconds\newline

Full solution

Q. A piece of ice falls off the side of a glacier and into the ocean. Its height above the ocean in meters can be modeled by the expression 334.9t233 - 4.9t^2, where tt is the time in seconds after the piece of ice begins to fall.\newlineWhat does the quantity 4.9t24.9t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the piece of ice to reach a height of tt meters\newline(B)the distance in meters the piece of ice has fallen after tt seconds\newline(C)the time in seconds it takes for the piece of ice to fall tt meters\newline(D)the height in meters of the piece of ice above the ocean after tt seconds\newline
  1. Initial Height Explanation: The expression for the height of the ice above the ocean is 334.9t233 - 4.9t^2. We know that the initial height is 3333 meters, so the 4.9t24.9t^2 must represent the distance the ice has fallen after tt seconds due to gravity.
  2. Derivation of 4.9t24.9t^2: The term 4.9t24.9t^2 is derived from the physics equation for free fall under gravity, which is s=12gt2s = \frac{1}{2}gt^2, where gg is the acceleration due to gravity (9.8m/s29.8 \, \text{m/s}^2 on Earth), ss is the distance fallen, and tt is the time in seconds. Here, 4.94.9 is half of 9.89.8, indicating that the expression accounts for the acceleration due to gravity.
  3. Corresponding Distance Explanation: Since 4.9t24.9t^2 represents the distance fallen, it corresponds to choice (B) the distance in meters the piece of ice has fallen after tt seconds.

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