There is a crater of depth R/100 on the surface of the moon (radius R). A Projectile is fired vertically upward from the crater with velocity, which is equal to the escape velocity v from the surface of the moon. Find the maximum height attained by the projectile.

Speed of particle at A,vA = escape velocity on the surface of earth =2GMRAt highest point B,  vB = 0Applying conservation of mechanical energy, decrease in kinetic energy = increase in gravitational potential energy=12mvA2=UB−UA=mVB−VAvA22=VB−VAGMR=−GMR+h−−GMR31.5R2−0.5R−R10021R=−1R+h+32R−12991002⋅1RSolving this equation, we get h = 99.5R