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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 $30$ feet, it starts to fall back down. The ball's height above the ground in feet can be modeled by the expression $30 - 16t^2$ , where $t$ is the time in seconds after the ball starts to fall back down. $\newline$ What does the quantity $16t^2$ represent in the expression? $\newline$ Choices: $\newline$ (A)the time in seconds it takes for the ball to fall $t$ feet $\newline$ (B)the time in seconds it takes for the ball to reach a height of $t$ feet $\newline$ (C)the distance in feet the ball has fallen after $t$ seconds $\newline$ (D)the height in feet of the ball above the ground after $t$ seconds $\newline$

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Interpret parts of quadratic expressions: word problems

Full solution

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

30

feet, it starts to fall back down. The ball's height above the ground in feet can be modeled by the expression

30 - 16t^2

, where

t

is the time in seconds after the ball starts to fall back down.

\newline

What does the quantity

16t^2

represent in the expression?

\newline

Choices:

\newline

(A)the time in seconds it takes for the ball to fall

t

feet

\newline

(B)the time in seconds it takes for the ball to reach a height of

t

feet

\newline

(C)the distance in feet the ball has fallen after

t

seconds

\newline

(D)the height in feet of the ball above the ground after

t

seconds

\newline

Initial Height Explanation: The expression for the ball's height is $30 - 16t^2$ . We know that the initial height is $30$ feet.
Height Loss Calculation: The term $16t^2$ must represent how much height the ball loses over time since it's being subtracted from the initial height.
Gravity Formula Introduction: In physics, the formula for the distance an object falls due to gravity is $(\frac{1}{2})gt^2$ , where $g$ is the acceleration due to gravity ( $32$ feet per second squared on Earth).
Gravitational Constant Usage: The expression $16t^2$ is half of $32$ , which means it's using the gravitational constant. So, $16t^2$ is the distance the ball has fallen after $t$ seconds.

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