# A rocket whose initial mass is 850 kg consumes fuel at the rate of 2.3 kgs-1, The speed of the exhaust gases relative to the rocket engine is 2000 ms-

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A rocket whose initial mass is 850 kg consumes fuel at the rate of 2.3 kgs-1, The speed of the exhaust gases relative to the rocket engine is 2000 ms-1. What thrust does the rocket engine provide?

1. 5.47 x 106 N
2. 4600 N
3. 1217 N
4. 6440 N

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Correct Answer - Option 2 : 4600 N

The correct answer is 4600 N.

CONCEPT:

• Rocket: A rocket works by expelling gases from one end at a very high velocity.
• The escaping gas has a very high speed and this with its mass translates to a very large momentum. due to the principle of conservation of momentum the body of the rocket is pushed forward.
• The propulsion of all rockets is explained by Newton's third law of motion.
• A rocket's acceleration depends on three major factors:
• Exhaust velocity
• Rate the exhaust is ejected
• Mass of the rocket

The amount of thrust (Ft) produced by the engine is given by:

F= v × $\frac{dm}{dt}$

Where v is the speed of exhaust gases with respect to rocket and $\frac{dm}{dt}$ is fuel consumption rate or mass per unit time

The acceleration (a) of the rocket is given by:

a = Ft/M

Where M is the mass of the rocket and Ft is the thrust

CALCULATION:

Given that:

M = 850 kg, Fuel consumption rate = $\frac{dm}{dt}$ = 2.3 kgs-1

Speed of the exhaust gases relative to the rocket engine (v) = 2000 ms-1

Thrust produced by the engine = F= v × $\frac{dm}{dt}$ = 2000 × 2.3 = 4600 N