A rocket exhausts fuel with a velocity of 1500 m/s, relative to the rocket.It starts from rest in outer space with fuel comprising 80 per cent of the total mass.When all the fuel has been exhausted its speed is:
A)3600 m/s
B)2400 m/s
C)1200 m/s
D)880 m/s
E)400 m/s

Question

Quizplus · Accepted Answer

To solve this problem, we can use the principle of conservation of momentum. In the absence of external forces (i.e. in outer space), the total momentum of the rocket and the fuel must be conserved.

Let's call the mass of the entire rocket (including fuel) M, and the mass of the fuel m. Initially, the rocket is at rest, so its momentum is zero. The total momentum of the fuel is:

Momentum of fuel = m x (velocity of fuel relative to rocket)

However, we also know that initially, the fuel comprises 80% of the total mass. Therefore, we can write:

Momentum of fuel = (0.8M) x (1500 m/s)

At the end of the burn, all the fuel is expelled from the rocket, so the momentum of the rocket must be equal in magnitude but opposite in direction to the initial momentum of the fuel. Let's call the final velocity of the rocket V. Then:

Final momentum of rocket = M x V

By conservation of momentum, we have:

Momentum of fuel = Final momentum of rocket

(0.8M) x (1500 m/s) = M x V

Solving for V, we get:

V = (0.8M x 1500 m/s) / M = 1200 m/s

Therefore, the answer is B) 2400 m/s.

A Rocket Exhausts Fuel with a Velocity of 1500 M/s