A nationwide interoperable public safety wireless broadband network is being planned by the First Responder Network Authority (FirstNet) under the auspices of the United States government. The public safety network shall provide the needed wireless coverage in the wake of an incident or a disaster. This paper proposes a network with airdropped sensors to provide network coverage over disaster areas where it is difficult for human beings to regularly deploy sensors. The rescue delay for the victims to announce their existence to or receive the notification from the sensors is discussed. Then the optimal ALOHA protocol and the minimum number of sensors are derived subject to the rescue delay requirement. The simulations compare the performance of different transmission modes specified by the modulation and coding rate. It is shown that the transmission mode should be carefully selected to balance the tradeoff between the lifetime and the cost of the public safety network.