A droplet of water drips from the end of a stalactite high up on the roof of a cave. The height of the water droplet above the cave floor in meters can be modeled by the expression $22 - 4.9t^2$ , where $t$ is the time in seconds after the water droplet begins to fall. $\newline$ What does the quantity $4.9t^2$ represent in the expression? $\newline$ Choices: $\newline$ (A)the distance in meters the water droplet has fallen after $t$ seconds $\newline$ (B)the time in seconds it takes for the water droplet to reach a height of $t$ meters $\newline$ (C)the time in seconds it takes for the water droplet to fall $t$ meters $\newline$ (D)the height in meters of the water droplet above the cave floor after $t$ seconds $\newline$

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Q. A droplet of water drips from the end of a stalactite high up on the roof of a cave. The height of the water droplet above the cave floor in meters can be modeled by the expression

22 - 4.9t^2

, where

t

is the time in seconds after the water droplet begins to fall.

\newline

What does the quantity

4.9t^2

represent in the expression?

\newline

Choices:

\newline

(A)the distance in meters the water droplet has fallen after

t

seconds

\newline

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

t

meters

\newline

(C)the time in seconds it takes for the water droplet to fall

t

meters

\newline

(D)the height in meters of the water droplet above the cave floor after

t

seconds

\newline

Height Expression Analysis: The expression for the height of the water droplet is $22 - 4.9t^2$ . We know that the initial height is $22$ meters, so the term $4.9t^2$ must represent the distance fallen after $t$ seconds, because as time increases, the height decreases.
Derivation of $4.9t^2$ : The term $4.9t^2$ is derived from the physics equation for the distance fallen under gravity, which is $(1/2)gt^2$ , where $g$ is the acceleration due to gravity ( $9.8 \, \text{m/s}^2$ ). So, $4.9$ is half of $9.8$ , which confirms that $4.9t^2$ is the distance fallen.
Confirmation of Distance Fallen: Since $4.9t^2$ represents the distance fallen, it matches with choice (A) the distance in meters the water droplet has fallen after $t$ seconds.