Question

a rock is dropped from a bridge over a river. which table represents the distance in feet fallen as a function of time in seconds? table a time (seconds) distance fallen (feet) 0 0 1 48 2 96 3 144 table b time (seconds) distance fallen (feet) 0 0 1 16 2 64 3 144 table c time (seconds) distance fallen (feet) 0 180 1 132 2 84 3 36 table d time (seconds) distance fallen (feet) 0 180 1 164 2 116 3 36 table a table c table b table d

Explanation:

Step1: Recall free - fall formula

The distance $d$ an object falls in free - fall (neglecting air resistance) is given by the formula $d = \frac{1}{2}gt^{2}$, where $g$ is the acceleration due to gravity. On Earth, $g\approx 32$ ft/s². So, $d = 16t^{2}$.

Step2: Calculate distances for different times

When $t = 0$, $d=16\times0^{2}=0$.
When $t = 1$, $d = 16\times1^{2}=16$.
When $t = 2$, $d=16\times2^{2}=16\times4 = 64$.
When $t = 3$, $d=16\times3^{2}=16\times9 = 144$.

Answer:

Table B