(b) A compressed gas nozzle ejects gas at mass flow rate in (in kg/s) and velocity v (in m/s). The force (in N) exerted by the ejected gas is F=mv. A spacecraft has three identical compressed gas nozzles (N1, N2 and N3) located as shown in the diagram below. y N N N3 X Suppose that the mass flow rate in = 5 kg/s, the gas velocity v = 25 m/s and the mass of the spacecraft is 300 kg. All three nozzles are activated simultaneously for 15 s and then shut off. The x and y axes are as shown in the diagram and the spacecraft is initially located at (0,0) at rest. Ignore all forces other than those acting on the spacecraft from the nozzles and that the motion of the spacecraft is simple translation (i.e. no rotation). (i) Write the velocity of the spacecraft at time 15 s as a vector. (ii) What is the location P of the spacecraft at time 15 s? If nozzle N3 shuts off early after 8 s (rather than 15 s) how far from P will the spacecraft be at time 15 s?