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We address a resource constrained lifetime problem in sensor networks in an operating environment where nodes can be physically destroyed. Specifically, given a limited number of sensors and a hostile environment, our goal is to maximize the network lifetime and derive a node deployment plan. The problem of physical destruction, due to hostile environments and the small size of the sensors, is a viable threat and severely constrains the practical lifetime of sensor networks. The lifetime problem we define is representative, practical, and encompasses other versions of similar problems. We also define a representative physical attack model under which we study and solve the lifetime problem. Our solutions take into account both node constraints and the goal of energy minimization. An important observation based on this work is that network lifetime is greatly affected by the presence of physical attacks, highlighting the importance of our study. Our work has a broad and immediate impact for system designers deploying networks in hostile environments.