What computer was designed for the US Army to calculate trajectories for bombing tables?

Answer 1

Perhaps your thinking of ENIAC, but no ENIAC was designed for calculating artillery firing tables.

Both the Norden and Sperry analog computer bombsights preceded ENIAC, but they are electromechanical not electronic. I don't know when the first electronic computer bombsight was made, but remember the Nordens were still in use in the Vietnam War! You can't use tables for bombing, the calculations must be done in real-time.