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A rocket of total initial mass mo is expelling exhaust gas at a steady speed 2.88 m /sec with respect to itself, when its mass is reduced to 1/2 m0, the velocity attained by the rocket will be ______ (in m/sec).
Correct answer is '2'. Can you explain this answer?
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Verified Answer
A rocket of total initial mass mo is expelling exhaust gas at a steady...
Formula for rocket is given as
putting in eq.(1) we get
putting in eq.(1) we get
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A rocket of total initial mass mo is expelling exhaust gas at a steady...
Problem:
A rocket of total initial mass mo is expelling exhaust gas at a steady speed 2.88 m/sec with respect to itself. When its mass is reduced to 1/2 mo, the velocity attained by the rocket will be ______ (in m/sec). Correct answer is '2'. Can you explain this answer?
Solution:
To find the velocity attained by the rocket when its mass is reduced to 1/2 mo, we can use the principle of conservation of momentum.
Conservation of Momentum:
According to the principle of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it.
In this case, the rocket and the exhaust gas form an isolated system. Initially, the rocket has a total mass of mo and the exhaust gas has a mass of 0. When the rocket expels exhaust gas, the total mass of the system reduces to 1/2 mo.
Step 1: Initial Momentum:
The initial momentum of the system can be calculated as the product of the initial total mass and the velocity of the rocket with respect to itself.
Initial momentum = mo * 2.88 m/sec
Step 2: Final Momentum:
The final momentum of the system can be calculated as the product of the final total mass and the velocity of the rocket after the mass reduction.
Final momentum = (1/2 mo) * V
where V is the velocity attained by the rocket.
Step 3: Conservation of Momentum:
According to the principle of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system.
mo * 2.88 m/sec = (1/2 mo) * V
Simplifying the equation, we can find the value of V:
2.88 m/sec = (1/2) * V
V = 2 * 2.88 m/sec
Thus, the velocity attained by the rocket when its mass is reduced to 1/2 mo is 2 m/sec.
A rocket of total initial mass mo is expelling exhaust gas at a steady speed 2.88 m/sec with respect to itself. When its mass is reduced to 1/2 mo, the velocity attained by the rocket will be ______ (in m/sec). Correct answer is '2'. Can you explain this answer?
Solution:
To find the velocity attained by the rocket when its mass is reduced to 1/2 mo, we can use the principle of conservation of momentum.
Conservation of Momentum:
According to the principle of conservation of momentum, the total momentum of an isolated system remains constant if no external forces act on it.
In this case, the rocket and the exhaust gas form an isolated system. Initially, the rocket has a total mass of mo and the exhaust gas has a mass of 0. When the rocket expels exhaust gas, the total mass of the system reduces to 1/2 mo.
Step 1: Initial Momentum:
The initial momentum of the system can be calculated as the product of the initial total mass and the velocity of the rocket with respect to itself.
Initial momentum = mo * 2.88 m/sec
Step 2: Final Momentum:
The final momentum of the system can be calculated as the product of the final total mass and the velocity of the rocket after the mass reduction.
Final momentum = (1/2 mo) * V
where V is the velocity attained by the rocket.
Step 3: Conservation of Momentum:
According to the principle of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system.
mo * 2.88 m/sec = (1/2 mo) * V
Simplifying the equation, we can find the value of V:
2.88 m/sec = (1/2) * V
V = 2 * 2.88 m/sec
Thus, the velocity attained by the rocket when its mass is reduced to 1/2 mo is 2 m/sec.
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Community Answer
A rocket of total initial mass mo is expelling exhaust gas at a steady...
U=2.88 m/sec
m/mo=1/2
or
mo/m= 2/1
By
v= u ln(mo/m)
= 2.88 ln(2)
= 2.88( 0.693)
= 1.98~2
m/mo=1/2
or
mo/m= 2/1
By
v= u ln(mo/m)
= 2.88 ln(2)
= 2.88( 0.693)
= 1.98~2
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A rocket of total initial mass mo is expelling exhaust gas at a steady speed 2.88m /sec with respect to itself, when its mass is reduced to 1/2 m0,the velocityattained by the rocket will be ______ (in m/sec).Correct answer is '2'. Can you explain this answer?
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