The height of the ledge and acceleration due to gravity.
Explanation
The motion of an object falling freely under the influence of gravity is governed by the kinematic equations of motion. Specifically, this scenario represents uniformly accelerated motion where the acceleration is equal to the acceleration due to gravity ($g$).
Analysis:
According to the second equation of motion:
$$s = ut + \frac{1}{2}at^2$$
Where:
- $s$ is the displacement (vertical height, $h$).
- $u$ is the initial vertical velocity (0, as the car falls from rest).
- $a$ is the acceleration due to gravity ($g$).
- $t$ is the time taken.
$$h = 0 + \frac{1}{2}gt^2$$
Rearranging for time ($t$):
$$t = \sqrt{\frac{2h}{g}}$$
From this relationship, it is evident that the time of fall depends exclusively on the height ($h$) and the acceleration due to gravity ($g$). The mass, density, or horizontal dimensions (width of the ledge) do not influence the time taken to reach the ground in the absence of significant air resistance.
Key Takeaway:
For a body in free fall (neglecting air resistance), the time taken to reach the ground is independent of the body's mass or physical properties and is determined solely by the vertical height and the local acceleration due to gravity.