Question

a group of students are conducting an experiment on free - fall motion by dropping bricks from different heights out of the window of a building. they drop a brick from a window that is 20 m high and it takes t seconds to fall to the ground. the second trial they drop an identical brick from a window of a building that is 80 m high. air resistance is negligible. how will it take to fall to the ground?
a. 1 seconds
b. 2t seconds
c. 4t seconds
d. 10t seconds

Explanation:

Step1: Identify the free - fall formula

The formula for the height of a free - falling object is $h = v_0t+\frac{1}{2}gt^2$. Since the brick is dropped (initial velocity $v_0 = 0$), the formula simplifies to $h=\frac{1}{2}gt^2$, where $h$ is the height, $g$ is the acceleration due to gravity ($g = 9.8\ m/s^2$), and $t$ is the time of fall.
For the first drop, $h_1 = 20\ m$ and $t_1=T$, so $20=\frac{1}{2}gT^2$.
For the second drop, $h_2 = 80\ m$ (since the height is 4 times the first height as $80 = 4\times20$), and $h_2=\frac{1}{2}gt_2^2$.

Step2: Find the relationship between the two times

From $h_1=\frac{1}{2}gT^2$ and $h_2=\frac{1}{2}gt_2^2$, and $h_2 = 4h_1$.
Substituting $h_1$ and $h_2$ into the equations: $\frac{1}{2}gt_2^2=4\times\frac{1}{2}gT^2$.
Cancel out $\frac{1}{2}g$ on both sides, we get $t_2^2 = 4T^2$.
Taking the square - root of both sides (we consider the positive root since time cannot be negative), $t_2 = 2T$.

Answer:

2T seconds