Question

10. A rocket of mass 20kg has 180 kg of fuel.
The exhaust velocity of fuel is 1.6 km/sec.
Calculate the ultimate velocity of the rocket
gained, when the rate of consumption of the
fuel is 2kg/sec. (neglect gravity)​

Answer 1

Answer:

Explanation:

v=u ln(M/M-rt)

wher M is the total mass of rocket + fuel at t=0 sec = 20 +180 =200 kg

and r rate of fuel consumption =2kg/sec

u is the velocity of gas ejection w.r.t rocket = 1.6 km/sec

 

ultimate velocity is achieved when all the fuel will burn

ie. M-rt =20 kg

so v= 1.6 ln(180/20)

       =3.515 km/sec

Answer 2

The ultimate velocity of the rocket gained, when the rate of consumption of the fuel is 2kg/sec is 3.68 m/s.

Given:

Rocket (m)= 20 Kg , Mass of Fuel = 180 Kg, $V_{r} = 1.6 Km/sec$

To Find:

The ultimate velocity of the rocket gained.

Solution:

Total mass(M) = mass of rocket(m) + mass of fuel

= 20 + 180

=200 Kg.

The rate of consumption of the fuel(r) is 2kg/sec .

Ultimate Velocity = $v_{r} ln(\frac{M}{m} )$

= $1.6 ln (\frac{200}{20} )$

=$1.6 *2.303 * log (20)$

=$1.6 * 2.303$

= 3.68 m/s.

The ultimate velocity of the rocket gained, when the rate of consumption of the fuel is 2kg/sec is 3.68 m/s.

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