Question

how to solve this problem... Let's imagine a rocket. Let's say that the radius of the Earth is R. With the speed of v1, it goes up until the distance between the rocket and the ground is R. With the speed of v2, it can escape the Earth. what's v1/v2?

Answer 1

well, let's first find out v1.
Let's say that the mass of the
Earth is M and the mass of the rocket v2.

1/2m(v1)^2-GMm/R=-GMm/2R
v1=\[\sqrt{GM/R}\]

Again, we should use the energy conservation law to know what v2 is.
1/2mv2^2-GMm/R=0
v2=\[\sqrt{2GM/R}\]

So.. v1/v2=\[ \frac{ 1 }{\sqrt{2}}\]

Answer 2

thanks a lot