A rocket for use in deep space is to be capable of boosting a total load (payload plus the rocket frame and engine) of 2.95 metric tons to a speed of 10,000 m/s. (a) It has an engine and fuel designed to produce an exhaust speed of 2800 m/s. How much fuel plus oxidizer is required? metric tons (b) If a different fuel and engine design could give an exhaust speed of 8400 m/s, what amount of fuel and oxidizer would be required for the same task? metric tons (c) Noting that the exhaust speed in part (b) is 3.00 times higher than that in part (a), explain why the required fuel mass is not simply smaller by a factor of 3.00.

A rocket for use in deep space is to be capable of boosting a total load (payload plus the rocket frame and engine) of 2.95 metric tons to a speed of 10,000 m/s. (a) It has an engine and fuel designed to produce an exhaust speed of 2800 m/s. How much fuel plus oxidizer is required? metric tons (b) If a different fuel and engine design could give an exhaust speed of 8400 m/s, what amount of fuel and oxidizer would be required for the same task? metric tons (c) Noting that the exhaust speed in part (b) is 3.00 times higher than that in part (a), explain why the required fuel mass is not simply smaller by a factor of 3.00.