As its?a gravity free space, if we take the ball and the man as the system then?there?is no external force acting on them so CONSERVATION OF MOMENTUM IS POSSIBLE!!
The principle of conservation of momentum says that in the absence of any external force ( in an isolated?system ) the net momentum is always the same.
Initial momentum = Final momentum.
Here Initial?momentum is Zero for the system and thus , final momentum should also be zero!
Let M1?and M2?be the masses of the man and the stone?respectively and let V1?and V2?be their respective velocities after the man throws the stone.
According to the principle of conservation of momentum :-
M1V1=M2V2
so 50(v)=0.5(2)
therefore v= 0.02 m/sec. This is the velocity of man opposite to the velocity of stone so as to make the net momentum zero!
Now calculating?time taken by stone?to reach floor :-
As velocity= displacement / time
so time comes out to be = 5 sec
In these 5 sec?the man travels some distance as he is also having some velocity!
Distance travelled by man from where he dropped the stone?= velocity (man) * time = 0.02*5 m= 0.1 m
so distance between man and stone?is = 10 m + 0.1 m=?10.1 m
That's why? when the stone reaches the floor , the man is 10.1 m above the floor.
