Extend CQ and AB to point E and connect DE.

∵Q is the center of gravity, ∴ E and D are the midpoint of AB and AC respectively.

∴DE is the center line of △ABC, de∨BC, DE:BC= 1:2.

DQ:QB=DE:BC= 1:2

∴Q is the bisector of BD, and BQ=(2/3)BD.

According to Pythagorean theorem, AC= 12.

∴DC=6

According to Pythagorean theorem, in Rt△BCD, BD= the square root of 6 1.

∴BQ=(2/3) Times (the square root of 6 1)