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A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2?
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A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 k...
Given:
Initial mass of the rocket, m = 1500 kg
Gas ejected per second, u = 10 kg/s
Relative speed of the ejected gas, v = 5 km/s
Time elapsed after the blast, t = 50 s
To find: Acceleration of the rocket after 50 seconds neglecting gravity
Formula used:
From the law of conservation of momentum, the change in momentum of the rocket is equal to the momentum of the ejected gas.
Change in momentum of rocket = Momentum of ejected gas
m * Δu = u * (m - Δm) * v
where,
Δu = gas ejected in time t = u * t
Δm = mass of gas ejected in time t = Δu
m = initial mass of rocket
Simplifying the above equation, we get
Δm = m * (1 - e^(-u*t/m))
where,
e = 2.71828 (constant)
t = 50 s
The acceleration of the rocket is given by
a = (u * v - Δu * v) / m
Substituting the values, we get
a = (10 * 5 - (10 * 50 * e^(-10*50/1500)) * 5) / 1500
Solving the above equation, we get
a = 25 m/s^2
Therefore, the acceleration of the rocket after 50 seconds neglecting gravity is 25 m/s^2.
Answer: 2) 25m/s^2
Initial mass of the rocket, m = 1500 kg
Gas ejected per second, u = 10 kg/s
Relative speed of the ejected gas, v = 5 km/s
Time elapsed after the blast, t = 50 s
To find: Acceleration of the rocket after 50 seconds neglecting gravity
Formula used:
From the law of conservation of momentum, the change in momentum of the rocket is equal to the momentum of the ejected gas.
Change in momentum of rocket = Momentum of ejected gas
m * Δu = u * (m - Δm) * v
where,
Δu = gas ejected in time t = u * t
Δm = mass of gas ejected in time t = Δu
m = initial mass of rocket
Simplifying the above equation, we get
Δm = m * (1 - e^(-u*t/m))
where,
e = 2.71828 (constant)
t = 50 s
The acceleration of the rocket is given by
a = (u * v - Δu * v) / m
Substituting the values, we get
a = (10 * 5 - (10 * 50 * e^(-10*50/1500)) * 5) / 1500
Solving the above equation, we get
a = 25 m/s^2
Therefore, the acceleration of the rocket after 50 seconds neglecting gravity is 25 m/s^2.
Answer: 2) 25m/s^2
Community Answer
A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 k...
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A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2?
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A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2?.
A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of initial mass 1500 kg ejects gas at a constant rate of 10 kgs-1 with a relative speed of 5 kms-1 .The acceleration of the rocket 50 seconds after the blast, neglecting gravity 1) 10m/s^2 2) 25m/s^2 3 50m/s^2 4) 100m/s^2?.
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