Escape velocity of a projectile from the Earth, vesc = 11.2 km/s
Projection velocity of the projectile, vp = 3vesc
Mass of the projectile = m
Velocity of the projectile far away from the Earth = vf
Total energy of the projectile on the Earth
Gravitational potential energy of the projectile far away from the Earth is zero.
Total energy of the projectile far away from the Earth
From the law of conservation of energy, we have