Answer
2.79
Work Step by Step
We know that the kinetic energy is the result of a change in potential energy. Thus, in order to solve this problem, we use conservation of energy. Doing this, we find:
$\frac{1}{2}mv_f^2 + U_f=\frac{1}{2}mv_0^2 +U_0$
$\frac{1}{2}mv_f^2 -\frac{GMm}{R_e+22,000}=\frac{1}{2}mv_0^2 -\frac{GMm}{r}$
Plugging in the known values, we find:
$r = 4.185 \times10^{11}=2.79 \ AU$
