Solve the below problem:
Q: A 5000-lb probe in orbit about the moon is 8 ft high and has octagonal bases of sides 4 ft. The coordinate axes shown are the principal centroidal axes of inertia of the probe, and its radii of gyration are kx = 2.45 ft, ky = 2.65 ft, and kz = 2.55 ft. The probe is equipped with a main 125-lb thruster E and with four 5-lb thrusters A, B, C, and D which can expel fuel in the positive y direction. The probe has an angular velocity ω= (0.040 rad/s)i + (0.060 rad/s)k when two of the 5-lb thrusters are used to reduce the angular velocity to zero. Determine
(a) Which of the thrusters should be used?
(b) The operating time of each of these thrusters,
(c) For how long the main thruster E should be activated if the velocity of the mass center of the probe is to remain unchanged.
