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When I had these kinds of problems, the first thing I attempted to fix (usually successfully) was the source of the projectiles. Getting your client calmed down, sometimes by explaining that you have always been able to fix these things (don't say eventually, even if true). Once that front is under control, you have one (or more) less distractions and can concentrate on what you do well, fixing the actual problem. Appearing to be hard at work sometimes helps to keep the projectiles from returning. Perception is nearly everything in these situations.