Clearly when both guns fire simultaneously, the truck will remain stationary and under these conditions (firing from a stationary platform), the shells hit their target. If one of the guns fires sooner than the other, then, in accordance with the law of conservation of momentum, the truck will begin to move in the opposite direction. Since all the conditions governing the motion of the shell remain the same in the barrel of the gun, while the barrel itself begins to move, together with the truck, in the opposite direction (and this motion begins in conjunction with the
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shell, i.e, while it is still in the barrel of the gun); the shell will leave the barrel with a velocity relative to the earth, which is reduced by comparison with its velocity when fired from a stationary platform. Therefore the shell will fall short of its target. The platform's motion will continue right up to the firing of the second gun. Therefore, when it is fired, the second gun's barrel will be moving, together with the truck, in the same direction as its shot; thus the shell will have a slightly greater velocity when leaving the gun than if it had been fired from a stationary gun. Therefore it will overshoot its target.
Since the velocity of the second shell when fired is greater than that of the first, it follows from the law of conservation of momentum that after the second shot is fired the truck must begin to move in a direction opposite to the direction of the shot. For simplification, we do not take into account the circumstance that after firing the gun's barrel will move relative to the gun carriage. But it is clear that this will not, in principle, change the part played by the truck's movement.