Example 2.9 : A balloon is equipped with temperature- andaltitude-measuring instruments and has radio equipment that can transmit the outputreadings of these instruments back to ground. The balloon is initially anchored to theground with the instrument output readings in steady-state. The altitude-measuringinstrument is approximately zero order and the temperature transducer first-order with atime constant of 15 seconds. The temperature on the ground, T, is 10 °C and thetemperature T, at an altitude of x meters is given by the relation: T, = T,- 0.01x.0'(a) If the balloon is released at time 0, and thereafter rises upward at a velocity of 5 m/s,draw a table showing the temperature and altitude measurements reported at intervals of10 seconds over the first 50 seconds of travel. Show also in the table the error in eachtemperature reading.(b) What temperature does the balloon report at an altitude of 5000 m?Solution:Let the temperature reported by the balloon at some general time t be T, Then, T, isrelated to T, by the relation:

Given, ground temperature T0=10°CTx=T0-0.01xvelocity u=5m/s

Answered: . Example 2.9 : A balloon is equipped…

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