First we write down the relevant information given in the question. Re = 6,400km = 6.4 x 106 m, Me = 6 x 1024 kg.For the projectile to escape the Earths gravity, the projectile must be launched with a kinetic energy which is greater than the amount of work needed to overcome Earths gravity, or Earth's gravitational potential. To find the minimum velocity required, we equate kinetic energy and gravitational potential on Earths surface and rearrange for velocity.
-GMm/R = 0.5mv2
Hence, v2 = -2GM/R, so vesc = sqrt(-2GM/R)Inputting the values gives an escape velocity of vesc = 11200 ms-1 to 3 s.f