Help me, please.

Anyone would do.

This question belongs to Mechanics thread.  It is answered there.  However, I have reproduced the same below:

We can use law of conservation of angular momentum and law of conservation of mechanical energy to solve this problem.

Initial angular momentum L_i = mvb

Final angular momentum L_f = mVR (assuming that the mass m will just graze the surface of earth, as per requirement of the problem statement).

Initial Potential Energy U_i = 0

Final Potential Energy

Initial Kinetic Energy

Final Kinetic Energy

Substituting the values in and solving for b,

we get