# Which freely falling object will hit the ground first ?

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If we drop a 100 kg and 1 kg body at the same time from a certain height ? Which one will hit the ground first ?

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Both will take the same time, as time taken is independent of the object mass. It can be proved using equations of motion as below:-`
We know that, , equation of motion where v is the velocity, a and s are acceleration and displacement respectively and u is the initial velocity of the object.

In this case u=0, a=g, where g is acceleration due to gravity as its free falling body under gravity
and s=h , where h is the height from which the object is dropped.

Substituting, all these we get, ,  equation of motion modified. In this equation, the only variable factor is h i.e the height, rest all are constants. Hence, it is certain that the velocity(speed) and thus time only depends on the height from which the object is dropped and in this case height for both objects is the same and hence we have, both objects falling at same speed(velocity) and hence they will take the same time to hit the ground.