Does human behavior exploit deep and accurate knowledge about how the world works, or does it rely on shallow and often inaccurate heuristics? This fundamental question is rooted in a classic dichotomy in psychology: human intuitions about even simple scenarios can be poor, yet their behaviors can exceed the capabilities of even the most advanced machines. One domain where such a dichotomy has classically been demonstrated is intuitive physics. Here we demonstrate that this dichotomy is rooted in how physical knowledge is measured: extrapolation of ballistic motion is idiosyncratic and erroneous when people draw the trajectories but consistent with accurate physical inferences under uncertainty when people use the same trajectories to catch a ball or release it to hit a target. Our results suggest that the contrast between rich and calibrated versus poor and inaccurate patterns of physical reasoning exists as a result of using different systems of knowledge across tasks, rather than being driven solely by a universal system of knowledge that is inconsistent across physical principles.