(Solved): (20 points) The year is 3077 and the event is rocket-car racing. Your race team needs some key cal ...

(20 points) The year is 3077 and the event is rocket-car racing. Your race team needs some key calculations from you, the team's physicist, in order to secure the 3077 Interstellar Rocket Cup. The liquid fuel is exhausted through a nozzle (see figure) and the speed of the exhausting fuel at the entrance to the nozzle $$(0.500\mathrm{m}$$ inner diameter) is $$200\mathrm{m}/\mathrm{s}$$. The inner diameter of the nozzle at the smallest point is $$0.050\mathrm{m}$$. Treat the speed of the fuel at the smallest point of the nozzle as the exhaust speed. If it takes 15 seconds to eject the full $$150\mathrm{kg}$$ tank of rocket fuel, what is the thrust, $${\vec{F}}_{\text{thrust }}$$, provided by the rocket engine on the car?