Answer
The speed of body B relative to body A is $~~2\sqrt{\frac{Gm}{R_i}}$
Work Step by Step
In part (b), we found that the kinetic energy of each body is $~~\frac{Gm^2}{2R_i}$
We can find the speed of each body relative to us:
$K = \frac{1}{2}mv^2 = \frac{Gm^2}{2R_i}$
$v^2 = \frac{Gm}{R_i}$
$v = \sqrt{\frac{Gm}{R_i}}$
Since the two bodies are moving toward each other, the speed of body B relative to body A is double the speed of each body relative to us.
We can find the speed of body B relative to body A:
$v = 2\sqrt{\frac{Gm}{R_i}}$
The speed of body B relative to body A is $~~2\sqrt{\frac{Gm}{R_i}}$
