Answer
12,982 meters
Work Step by Step
We need to make the asteroid so that the velocity of the jumper is below the escape speed of the asteroid. Thus, we first find how fast a jumper that goes 3 meters up on earth is jumping using conservation of energy:
$\frac{1}{2}mv^2 = mgh \\ v=\sqrt{2gh}=\sqrt{2\times9.81\times3}=7.672 \ m/s$
We know the following equation for escape speed:
$v_{esc}=\sqrt{\frac{2GM}{r}}$
$v_{esc}=\sqrt{\frac{2G(\frac{4}{3}\pi r^3)(2500)}{r}}$
$ r = \sqrt{\frac{v_{esc}^2}{6666.67\pi G}}$
Plugging in the value for G (a constant) and v (found above) gives:
$r=9491 m$
This means that: $\fbox{d=12,982 meters}$
