Two small variable$-$thrust jets are actuated to keep the spacecraft angular velocity about the $z-$axis constant at ${}_0=1\mathrm{.}48ra\frac{d}{s}$ as the two telescoping booms are extended from $r_1=1\mathrm{.}17m$ to $r_2=3\mathrm{.}53m$ at a constant rate over a period of $144$ seconds. The small $13-kg$ experiment modules at the ends of the booms may be treated as particles, and the mass of the rigid booms is negligible. Determine the necessary thrust $T$ for each jet as a function of time where $t=0$ is the time when the telescoping action is begun. After you have the general expression for $T,$ answer the questions.

Questions:

Whent $=22s$:$,T=$

When $t=65s$:$,T=$

When $t=129s$:$.,T=N$