The Apollo Command and Service Module was an American spacecraft which sent astronauts to the moon between 1968 and 1972. The mass of the spacecraft itself, without propellant, (called the 'dry mass') was approximately 12,000 kg. The spacecraft carried with it 18,000 kg of propellant. When the spacecraft's engine is running, it can expel propellant out the back of the spacecraft at a velocity of 3,000 m/s (called 'exhaust velocity') and at a rate of 24 kg/s. If the spacecraft burns through all of its propellant, what will be its final velocity? (Assume its initial velocity in deep space is 0 m/s). Apollo 15 Command and Service Module in orbit around the moon, 1971. Hints: This can be solved using calculus, though that is not what I am expecting. You can also solve this "numerically', by calculating the change in momentum at specific time intervals and applying that change to the rocket's velocity at each step. For example, you may want to calculate the change in momentum every 30 seconds, or every second. The shorter the time interval in each step, the more accurate your final answer will be, though the more calculations you will need to perform. It may be helpful to use a spreadsheet program like Microsoft Excel or Google Sheets to compute your results. For full marks: Show a sample calculation. Include your spreadsheet (if applicable). Explain your reasoning. State your final conclusion