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On a family vacation at the beach, Harold throws a beach ball upward as high as he can. When the ball reaches a height of 3030 feet, it starts to fall back down. The ball's height above the ground in feet can be modeled by the expression 30−16t230 - 16t^2, where tt is the time in seconds after the ball starts to fall back down.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the ball to fall tt feet\newline(B)the time in seconds it takes for the ball to reach a height of tt feet\newline(C)the distance in feet the ball has fallen after tt seconds\newline(D)the height in feet of the ball above the ground after tt seconds\newline

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Q. On a family vacation at the beach, Harold throws a beach ball upward as high as he can. When the ball reaches a height of 3030 feet, it starts to fall back down. The ball's height above the ground in feet can be modeled by the expression 30−16t230 - 16t^2, where tt is the time in seconds after the ball starts to fall back down.\newlineWhat does the quantity 16t216t^2 represent in the expression?\newlineChoices:\newline(A)the time in seconds it takes for the ball to fall tt feet\newline(B)the time in seconds it takes for the ball to reach a height of tt feet\newline(C)the distance in feet the ball has fallen after tt seconds\newline(D)the height in feet of the ball above the ground after tt seconds\newline
  1. Initial Height Explanation: The expression for the ball's height is 30−16t230 - 16t^2. We know that the initial height is 3030 feet.
  2. Height Loss Calculation: The term 16t216t^2 must represent how much height the ball loses over time since it's being subtracted from the initial height.
  3. Gravity Formula Introduction: In physics, the formula for the distance an object falls due to gravity is (12)gt2(\frac{1}{2})gt^2, where gg is the acceleration due to gravity (3232 feet per second squared on Earth).
  4. Gravitational Constant Usage: The expression 16t216t^2 is half of 3232, which means it's using the gravitational constant. So, 16t216t^2 is the distance the ball has fallen after tt seconds.

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