1. The problem asks which expression best models the distance in feet traveled by an object $t$ seconds after it is dropped from the top of a tall building.
2. When an object is dropped (free fall) near the Earth's surface, the distance fallen after $t$ seconds is given by the formula:
$$d = \frac{1}{2}gt^2$$
where $g$ is the acceleration due to gravity, approximately 32 feet per second squared.
3. Substituting $g = 32$ ft/sĀ², we get:
$$d = \frac{1}{2} \times 32 \times t^2 = 16t^2$$
4. This formula means the distance fallen is proportional to the square of the time, and the coefficient 16 comes from half the acceleration due to gravity.
5. Therefore, the correct expression modeling the distance traveled is:
$$16t^2$$
6. Among the options given, this corresponds to option B.
Final answer: B. 16t^2
Distance Fall 8Ea346
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