A man of mass 60 kg is standing in a gravity free at a height of 12 m above the floor . HE throws a stone of mass 0.5 kg downwards with a speed of 4 m/s .when the stone reaches the floor its distance from the man above the floor will be??/

Hi,

Because the spae is gravity free so , the man can move freely.
Whys is this important is because of conservation of momentum principle.
As the stone is going downwards, the man will go upwards.
The momentum of both the bodies will be same but in opossite direction to conserve the initial momentum which is zero.
i.e. 60x = .5*4 = 2
x = 2/60 or 1/30 or .33 m/s or 33.33 cm/sec.
Now with the speed of 4m/s the stone will take 3 seconds to decend.
In those 4 seconds man will travel 1/3*4 mts upwards.
So the final distance between thoes two bodies after three seconds will be
12 + 4/3 = 40 / 3 mts.