Two bodies A and B separated by some distance on the ground are projected simultaneously in opposite directions towards each other. Body B is projected with a velocity of $20\,ms^{-1}$ at an angle of $45^\circ$ with the horizontal and body A is projected at an angle of $30^\circ$ with the horizontal. If the two bodies collide at a time of $\sqrt{2}\,s$ from the beginning of their motion, then the initial distance between the bodies A and B is nearly}