1. The problem statement, all variables and given/known data A rocket accelerates to speed v0 near the earth's surface,and then coasts upwards. Show that if v0 = 2sqrt(gR) where R is the Earth's radius, then very far from the earth the rockets speed will be v = sqrt(2gR) 2. Relevant equations The only equations I have thought of that may help are: Escape Velocity: v = sqrt(2GM/R) Gravitational potential energy: U= -GMm/r 3. The attempt at a solution I have attempted using energy conservation and solving for v, however the answer appears far from that required. This lead me to think that perhaps linear approximation may be required but I am unsure how I would apply (1+x)n = 1+nx for x<<1 in this problem.