Logical Puzzle : Which ball reaches the ground first


There are 2 balls of mass  4  kilos and 9 kilos respectively. For the sake of simplicity, say they are exactly the same shape and volume, so that air resistance on both is same.They are dropped from a bomber flying at the height of  980 meters. Which one hits the ground first ?

I bet you know that in vacuum both reach the ground at the same time, irrespective of their weights.  But here we have added air resistance.

[ Hint  : Don’t just apply the 3 equations of motion because all 3 of them are independent of Mass, so you will end up with the same result for both. ]

Answer :
The heavy one hits the ground first.

Both the balls will initially travel under an acceleration of g. However they will later reach terminal velocity and once they do, they will travel at the constant speed.  Since the terminal velocity is directly proportional to the under root ofmass, it will be 1.5 times more for heavier ball. While the lighter ball will continue at a much slower speed, the heavier one will lead at a higher terminal velocity.

You can do a calculation to find the time it takes each one to reach terminal velocity and the actual terminal velocity.

We have all heard how Galileo threw 2 stones of different weight from the tower of Pisa and recorded the time taken to reach ground , and it was same. It could be because the height was not enough for either stone to reach the terminal velocity, so both were subject to constant acceleration g.