Answer:
The time of fall of an object is dependent only on the height of fall for a given acceleration due to gravity and it is independent of the object's mass
Explanation:
The gravitational force acting on an object on Earth can be observed as the weight, 'W', of the object which is a function of the mass, 'm', of the object and the relationship between the gravitational force and the mass of the object is given as follows;
W = m × g
Where;
g = The acceleration due to gravitational force = Constant
The relationship between the speed, 'u', and therefore, the time, 't', with which an object falls, the distance or height of fall, 'h', and the acceleration of the motion, 'g' is given as follows;
h = u·t + 1/2·g·t²
Given that the initial velocity of the object, 'u', of the object allowed to fall is u = 0 m/s, we have;
h = u·t + 1/2·g·t² = 0 × t + 1/2·g·t²
h = 0 × t + 1/2·g·t² = 1/2·g·t²
h = 1/2·g·t²
t² = 2·h/g
t = √(2·h/g)
Therefore, the time, 't', it takes every object to fall from a height, 'h', is dependent only on the height, 'h', for a given acceleration due to gravity, 'g' and it is independent of the mass, 'm', of the object.
