Escape velocity of a projectile from the Earth, v_esc = 11.2 km/s
Projection velocity of the projectile, v_p = 3v_esc
Mass of the projectile = m
Velocity of the projectile far away from the Earth = v_f
Total energy of the projectile on the Earth = (1/2)mv_p² - (1/2)mv_esc²
Gravitational potential energy of the projectile far away from the Earth is zero.
Total energy of the projectile far away from the Earth = (1/2)mv_f²
From the law of conservation of energy, we have
(1/2)mv_p² - (1/2)mv_esc²  =  (1/2)mv_f²
v_f = ( v_p² - v_esc² )^1/2
= [ (3v_esc)² - v_esc² ]^1/2
= √8 v_esc
= √8 × 11.2  =  31.68 km/s.