The radius of the Earth is 6,400km and has a mass of 6x10^24kg. Calculate the minimum velocity needed by a projectile, fired from the surface of the Earth in order to escape the Earths gravity.

First we write down the relevant information given in the question. R_e = 6,400km = 6.4 x 10⁶ m, M_e = 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 v_esc = sqrt(-2GM/R)Inputting the values gives an escape velocity of v_esc = 11200 ms^-1 to 3 s.f