Hello, Can someone please walk me through this problem, I\'m very confused. A ro

Question

Hello,
Can someone please walk me through this problem, I'm very confused.

A rocket car is developed to break the land speed record along a salt flat in Utah. However, the safety of the driver must be considered, so the acceleration of the car must not exceed5g(or five times the acceleration of gravity) during the test. Using the latest materials and technology, the total mass of the car(including the fuel) is 6000 kilograms, and the mass of the fuel is one-third of the total mass of the car (i.e., 2000 killograms). The car is moved to the starting line (and left at rest), at which time the rocket is ignited. The rocket fuel is expelled at a constant speed of 900 meters per second relative to the car, and is burned at a constant rate until used up, which takes only 15 seconds.Ignore all effects of friction in this problem.

Find the final velocity v_final of the car just as the rocket is about to use up its fuel supply.

Explanation / Answer

Find the force the fuel puts on the rocket: The mass of 2000 kg of fuel is accelerated from zero to 900 m/s in 15 seconds. Therefore the acceleration is 900/15 = 60 m/s^2. The force is 2000 kg*60m/s^2 = 120,000 N. This 120,000 N force is what accelerates the rocket so: F = 120,000 N = 4000 kg * a. Then just solve for a: a = 120,000 N/4000 kg = 30 m/s^2. Your answer is 30 m/s^2.

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