An unmanned submarine is equipped with temperature and depth measuring

instruments and has radio equipment that can transmit the output readings of these instruments back to the surface. The submarine is initially floating on the surface of the sea with the instrument output readings in steady state. The depth- measuring instrument is approximately zero order and the temperature transducer first order with a time constant of 50 seconds. The water temperature on the sea surface, To, is 20C and the temperature T, at a depth of x metres is given by the relation: T, = Ty 0.01x (a) If the submarine starts diving at time zero, and thereafter goes down at a velocity of 0.5 metres/second, draw a table showing the temperature and depth measurements reported at intervals of 100 seconds over the first 500 seconds of travel. Show also in the table the error in each temperature reading. (b) What temperature does the submarine report at a depth of 1000 metres?