A maintenance satellite uses two small thrusters that fire in opposite directions along the same line, producing equal-magnitude forces that cancel so that the satellite coasts at constant velocity relative to a nearby space station. At an instant that we shall label t=0, one thruster shuts off completely while the other keeps firing with unchanged thrust.
Assume the following idealizations:
• The satellite is a rigid body of mass 520kg that can be treated as a point particle for translational motion.
• External forces other than the two thrusters are negligible.
• Motion is confined to one dimension ("forward" = +x direction).
Answer the questions that follow, using clear, well-reasoned explanations that reference fundamental principles of mechanics.
(a) Describe the net force acting on the satellite during the time interval t<0 and during the time interval immediately after t=0. State whether the satellite is in translational equilibrium during each interval and justify your answer.
(b) Describe qualitatively how the satellite’s velocity changes, if at all, for t>0. Explain the connection between the net force you identified in part (a) and the subsequent motion.
(c) Consider a small axis misalignment so that the active thruster’s force has a component Fy perpendicular to the original line of motion while its component Fx remains as described above. Explain how the velocity components in the x and y directions will evolve over time, referencing the concept of dimensional independence.