the escape velocity of a projectile on the surface of the Earth is 11.2 km per second a body is projected out with twice this speed what is the speed of the body far away from the Earth at infinity

Dear Student 

Let m be the mass of the projectile, R be the radius of the earth and M be the mass of the earth. Initial velocity, v_i = 2 × 11.2 km/s = 22400 m/s

Let the speed at far away distance from earth be v.

Now,

Total energy on the surface of the earth = total energy at far away distance

=> ½ mv_i² – GMm/R = ½ mv²

=> v_i² – 2gR = v²

=> v² = 22400² – 2 × 9.8 × 6400000 = 376320000

=> v = 19398.96 m/s = 19.3 km/s

Regards