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 33−4.9t2, where t is the time in seconds after the piece of ice begins to fall.What does the quantity 4.9t2 represent in the expression?Choices:(A)the time in seconds it takes for the piece of ice to reach a height of t meters(B)the distance in meters the piece of ice has fallen after t seconds(C)the time in seconds it takes for the piece of ice to fall t meters(D)the height in meters of the piece of ice above the ocean after t seconds
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 33−4.9t2, where t is the time in seconds after the piece of ice begins to fall.What does the quantity 4.9t2 represent in the expression?Choices:(A)the time in seconds it takes for the piece of ice to reach a height of t meters(B)the distance in meters the piece of ice has fallen after t seconds(C)the time in seconds it takes for the piece of ice to fall t meters(D)the height in meters of the piece of ice above the ocean after t seconds
Initial Height Explanation: The expression for the height of the ice above the ocean is 33−4.9t2. We know that the initial height is 33 meters, so the 4.9t2 must represent the distance the ice has fallen after t seconds due to gravity.
Derivation of 4.9t2: The term 4.9t2 is derived from the physics equation for free fall under gravity, which is s=21gt2, where g is the acceleration due to gravity (9.8m/s2 on Earth), s is the distance fallen, and t is the time in seconds. Here, 4.9 is half of 9.8, indicating that the expression accounts for the acceleration due to gravity.
Corresponding Distance Explanation: Since 4.9t2 represents the distance fallen, it corresponds to choice (B) the distance in meters the piece of ice has fallen after t seconds.
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