Thruster A is turned on and exerts an upward force of $60\,\text{N}$ on the spacecraft. Thruster C is also turned on and exerts a force of $220\,\text{N}$ to the left on the spacecraft. Calculate the resultant moment due to these forces about the centre of gravity.
State and explain whether the forces from A and C are a couple.
Thrusters A and C are now turned off and the spacecraft is at rest. Thruster B is switched on at time $t_1$, producing a constant force on the spacecraft until the fuel is exhausted at time $t_2$. As the fuel is consumed, the total mass of the spacecraft falls. On Fig. 2.2, sketch how the speed of the spacecraft varies with time from $t_1$ to $t_2$.
The spacecraft now divides into a carrier and a payload as shown in Fig. 2.3. During the split, an average force of $5500\,\text{N}$ acts on the payload for a time of $0.36\,\text{s}$. The velocity of the payload increases by $8.5\,\text{m s}^{-1}$ in the upward direction. The combined mass of the carrier and payload is $2.5 \times 10^3\,\text{kg}$. State the principle of conservation of momentum.
Show that the mass of the payload is $230\,\text{kg}$.
Calculate the magnitude of the change in velocity of the carrier.