prove that escape velocity from surface of earth is 11 2 km/sec - Physics - Gravitation

Question

prove that escape velocity from surface of earth is 11 2 km/sec

Nandakishore · Accepted Answer

energy initial = energy final
energy final= 0 at r= infinity
energy initial = potential energy initial + kinetic energy
initial
energy initial= 1/2m(vescape)^2 + (-GMm/R)=0
so,
vescape= √2GM/R
Substituing appropraite values
v=11 2 km/s

prove that escape velocity from surface of earth is 11.2 km/sec