Problem 11.29

11.29.

Conservation of energy again gives us our answer.
K_i + U_i = U_f
since K_f=0.
$\frac{1}{2}mv^{2} - \frac{GMm}{r_{1}} = -\frac{GMm}{r_{2}}$
and $r_{1} = R_{Io} ~=~ 1.82 \times 10^{6}m$
$r_{2} = R_{Io} + 70km ~=~ 1.89 \times 10^{6}m$
so, solving for v, we find
v = 492 m/s