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A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)?
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A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel i...
Ans.
Velocity of rocket is given as
v=u ln(M/M-rt)
when 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
Velocity of rocket is given as
v=u ln(M/M-rt)
when 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
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Most Upvoted Answer
A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel i...
Given data:
Mass of rocket (m) = 20 kg
Mass of fuel (m_fuel) = 180 kg
Exhaust velocity of fuel (v_e) = 1.6 km/s
Rate of fuel consumption (r) = 2 kg/s
Calculating the change in momentum:
The rocket experiences a change in momentum as the fuel is expelled with a certain velocity.
The momentum change (Δp) can be calculated using the following formula:
Δp = m_fuel * v_e
Substituting the given values:
Δp = 180 kg * 1.6 km/s
Converting km/s to m/s:
To ensure consistent units, we need to convert the velocity from km/s to m/s.
1 km/s = 1000 m/s
So, the exhaust velocity (v_e) becomes:
v_e = 1.6 km/s * 1000 m/s/km
Calculating the change in momentum (Δp):
Substituting the converted value of v_e:
Δp = 180 kg * 1.6 km/s * 1000 m/s/km
Calculating the rate of change of momentum:
Rate of change of momentum (F) can be calculated by dividing the momentum change (Δp) by the time taken (t):
F = Δp / t
Since the rate of fuel consumption is given, the time taken (t) can be calculated by dividing the mass of fuel consumed (r) by the rate of fuel consumption (r):
t = m_fuel / r
Substituting the given values:
t = 180 kg / 2 kg/s
Calculating the final velocity:
Finally, the ultimate velocity of the rocket (v) can be calculated by dividing the rate of change of momentum (F) by the mass of the rocket (m):
v = F / m
Substituting the calculated values of Δp and t:
v = (Δp / t) / m
Final calculation:
By substituting the values and calculating, the ultimate velocity of the rocket can be determined.
It is important to note that gravity has been neglected in this calculation, and therefore the resulting velocity is only applicable in the absence of gravity.
Mass of rocket (m) = 20 kg
Mass of fuel (m_fuel) = 180 kg
Exhaust velocity of fuel (v_e) = 1.6 km/s
Rate of fuel consumption (r) = 2 kg/s
Calculating the change in momentum:
The rocket experiences a change in momentum as the fuel is expelled with a certain velocity.
The momentum change (Δp) can be calculated using the following formula:
Δp = m_fuel * v_e
Substituting the given values:
Δp = 180 kg * 1.6 km/s
Converting km/s to m/s:
To ensure consistent units, we need to convert the velocity from km/s to m/s.
1 km/s = 1000 m/s
So, the exhaust velocity (v_e) becomes:
v_e = 1.6 km/s * 1000 m/s/km
Calculating the change in momentum (Δp):
Substituting the converted value of v_e:
Δp = 180 kg * 1.6 km/s * 1000 m/s/km
Calculating the rate of change of momentum:
Rate of change of momentum (F) can be calculated by dividing the momentum change (Δp) by the time taken (t):
F = Δp / t
Since the rate of fuel consumption is given, the time taken (t) can be calculated by dividing the mass of fuel consumed (r) by the rate of fuel consumption (r):
t = m_fuel / r
Substituting the given values:
t = 180 kg / 2 kg/s
Calculating the final velocity:
Finally, the ultimate velocity of the rocket (v) can be calculated by dividing the rate of change of momentum (F) by the mass of the rocket (m):
v = F / m
Substituting the calculated values of Δp and t:
v = (Δp / t) / m
Final calculation:
By substituting the values and calculating, the ultimate velocity of the rocket can be determined.
It is important to note that gravity has been neglected in this calculation, and therefore the resulting velocity is only applicable in the absence of gravity.
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A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)?
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A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)?.
A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of mass 20kg has 180kg of fuel the exhaust velocity of fuel is 1.6km per second calculate the ultimate velocity of the rocket gained when the rate of consumption of the fuel is 2kg per second (neglect gravity)?.
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