The escape speed of a projectile on the earth's surface is 11.2km/s. A body is projected out with thrice this speed, What is the speed of the body far away from the earth?ignore the presence of the sun and other planets. What's the answer for this numerical??

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 = 3 × 11.2 km/s = 33600 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 = 33600² – 2 × 9.8 × 6400000 = 1003520000

=> v = 31678.4 m/s = 31.7 km/s