Question

jimmy releases a weight from rest and it free - falls for 8 sec.
a) what distance did it fall?
eq: $d = \frac{1}{2}gt^{2}$
b) how fast (and what direction) is it going?

Explanation:

Step1: Identify the formula for distance

The formula for the distance $d$ of a free - falling object is $d=\frac{1}{2}gt^{2}$, where $g = 9.8\ m/s^{2}$ (acceleration due to gravity) and $t$ is the time of fall.

Step2: Calculate the distance

Substitute $g = 9.8\ m/s^{2}$ and $t = 8\ s$ into the formula:
$d=\frac{1}{2}\times9.8\times8^{2}=\frac{1}{2}\times9.8\times64 = 313.6\ m$

Step3: Identify the formula for final velocity

The formula for the final velocity $v$ of a free - falling object starting from rest is $v = gt$.

Step4: Calculate the final velocity

Substitute $g = 9.8\ m/s^{2}$ and $t = 8\ s$ into the formula:
$v=9.8\times8 = 78.4\ m/s$, and the direction is downward.

Answer:

a) $313.6\ m$
b) $78.4\ m/s$, downward