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)
The only equations I have thought of that may help are:
v = sqrt(2GM/R)
Gravitational potential energy:
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.