On another planet, the value of g is one-half the value on Earth. How is the time needed for an object to fall to the ground from rest on that planet related to the time required to fall the same distance on Earth?

Let us assume the object has mass and is released from height h at time t = 0. We also assume that the magnitude of initial velocity of the object is zero i.e v_0x = 0. We assume that the downward motion of the object is taken as positive. Also from the reference of observer, we assume that the object was thrown from initial position x₀ = 0.
The distance travelled by the object (say x) when it reaches the ground after time on Earth can be given as:

Equating the above assumptions, we have

However, if the object is freely falling, the acceleration it has is equal to the acceleration due to gravity, which for Earth is . Also the distance travelled by the object when it reaches the ground is equal to the height (say h) from which it is released.
Therefore, we have


We neglect the solution for negative time, therefore the value of time is given as:
…… (1)
The distance travelled by the object (say x) when it reaches the ground after time on Planet can be given as:

Equating the assumptions, we have

However, if the object is freely falling, the acceleration it has is equal to the acceleration due to gravity, which for Planet is g/ 2 . Also the distance travelled by the object when it reaches the ground is equal to the height (say h) from which it is released.
It is important to note that the distance travelled by the object on the planet is same as that on Earth.
Therefore, we have


We neglect the solution for negative time, therefore the value of time is given as:
…… (2)
Taking the ratio of equation (1) and equation (2), we have



Therefore we find that the time taken by the object to reach the ground on Earth is with that to the time taken to reach the ground on Planet with acceleration due to gravity of .