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If air resistance can be ignored, then both objects are moving under the same force: gravity. The force is directly proportional to the masses of the objects.

Thus if the masses are Mp and Mq

then Gp = k*Mp and Gq = k*Mq where Gp and Gq are the forces acting on the two bodies.


The acceleration of the two objects is inversely proportional to their masses. [F = m*a => a = F/M]

So acc(p) = Gp/Mp = (k*Mp)/Mp = k

and acc(q) = Gq/Mq = (k*Mq)/Mq = k

That is, the acceleration of the two bodies is the same. Consequently, because they start from rest from the same height, they will hit the ground at the same time.

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