When Picard finally manages to squeeze through the hole in the force-field, and confronts Soran, they have a brawl. The actual time elapsed from the confrontation to the launch (I choose these points as the emergence from The Nexus later to the point when everything is hopeless, respectively), is fifty seconds. When Kirk confronts him after the entire bit in The Nexus, it's actually two minutes and ten seconds before Soran cloaks the missile, and another forty before is launches again after it's been uncloaked.