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A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.
Correct answer is '5837.75'. Can you explain this answer?
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A rocket, with an initial mass of 3000kg, is launched vertically upwar...
We know that velocity equation is givven by 
The maximum velocity of the rodect is
The maximum velocity of the rodect is
Most Upvoted Answer
A rocket, with an initial mass of 3000kg, is launched vertically upwar...
Given:
Mass of the rocket, m = 3000 kg
Rate of fuel burn, r = 40 kg/s
Velocity of ejected water, v = 4000 m/s (relative to the rocket)
Burning stops after one minute.
To find:
Maximum velocity of the rocket
Assumptions:
1. The rocket is launched vertically upwards.
2. The gravitational force is the only external force acting on the rocket.
Explanation:
Step 1: Find the initial acceleration of the rocket:
The rocket is initially at rest, so its initial velocity, u = 0 m/s.
Using Newton's second law of motion, F = ma, where F is the net force acting on the rocket and a is its acceleration.
The net force acting on the rocket is the gravitational force, given by F = mg, where g is the acceleration due to gravity.
Thus, ma = mg
=> a = g = 9.8 m/s^2 (assuming the acceleration due to gravity is approximately 9.8 m/s^2)
Step 2: Find the change in mass of the rocket:
The rocket burns fuel at a rate of 40 kg/s for one minute.
The change in mass of the rocket can be calculated using the formula:
Change in mass = rate of fuel burn × time
=> Change in mass = 40 kg/s × 60 s = 2400 kg
Step 3: Find the change in momentum of the rocket:
The change in momentum of the rocket is equal to the momentum of the ejected water.
The momentum of an object is given by the product of its mass and velocity.
Change in momentum = mass of ejected water × velocity of ejected water
=> Change in momentum = 2400 kg × 4000 m/s = 9,600,000 kg·m/s
Step 4: Find the final velocity of the rocket:
The final velocity of the rocket can be calculated using the principle of conservation of momentum.
According to this principle, the change in momentum of an object is equal to the impulse acting on it.
Impulse = Force × Time
=> Change in momentum = Force × Time
=> Force = Change in momentum / Time
=> Force = 9,600,000 kg·m/s / 60 s = 160,000 N
The net force acting on the rocket is the difference between the gravitational force and the force due to the ejected water.
Net force = mg - force due to ejected water
=> Net force = mg - (rate of fuel burn × velocity of ejected water)
=> Net force = 3000 kg × 9.8 m/s^2 - (40 kg/s × 4000 m/s)
=> Net force = 29,400 N
Using Newton's second law of motion, F = ma, where F is the net force acting on the rocket and a is its acceleration.
29,400 N = 3000 kg × a
=> a = 9.8 m/s^2 (approximately)
The final velocity of the rocket can be calculated using the equation of motion:
v^2 = u^2 + 2as
=> v^2 = 0 + 2 × 9.8 m/s^2 × s (where s is the
Mass of the rocket, m = 3000 kg
Rate of fuel burn, r = 40 kg/s
Velocity of ejected water, v = 4000 m/s (relative to the rocket)
Burning stops after one minute.
To find:
Maximum velocity of the rocket
Assumptions:
1. The rocket is launched vertically upwards.
2. The gravitational force is the only external force acting on the rocket.
Explanation:
Step 1: Find the initial acceleration of the rocket:
The rocket is initially at rest, so its initial velocity, u = 0 m/s.
Using Newton's second law of motion, F = ma, where F is the net force acting on the rocket and a is its acceleration.
The net force acting on the rocket is the gravitational force, given by F = mg, where g is the acceleration due to gravity.
Thus, ma = mg
=> a = g = 9.8 m/s^2 (assuming the acceleration due to gravity is approximately 9.8 m/s^2)
Step 2: Find the change in mass of the rocket:
The rocket burns fuel at a rate of 40 kg/s for one minute.
The change in mass of the rocket can be calculated using the formula:
Change in mass = rate of fuel burn × time
=> Change in mass = 40 kg/s × 60 s = 2400 kg
Step 3: Find the change in momentum of the rocket:
The change in momentum of the rocket is equal to the momentum of the ejected water.
The momentum of an object is given by the product of its mass and velocity.
Change in momentum = mass of ejected water × velocity of ejected water
=> Change in momentum = 2400 kg × 4000 m/s = 9,600,000 kg·m/s
Step 4: Find the final velocity of the rocket:
The final velocity of the rocket can be calculated using the principle of conservation of momentum.
According to this principle, the change in momentum of an object is equal to the impulse acting on it.
Impulse = Force × Time
=> Change in momentum = Force × Time
=> Force = Change in momentum / Time
=> Force = 9,600,000 kg·m/s / 60 s = 160,000 N
The net force acting on the rocket is the difference between the gravitational force and the force due to the ejected water.
Net force = mg - force due to ejected water
=> Net force = mg - (rate of fuel burn × velocity of ejected water)
=> Net force = 3000 kg × 9.8 m/s^2 - (40 kg/s × 4000 m/s)
=> Net force = 29,400 N
Using Newton's second law of motion, F = ma, where F is the net force acting on the rocket and a is its acceleration.
29,400 N = 3000 kg × a
=> a = 9.8 m/s^2 (approximately)
The final velocity of the rocket can be calculated using the equation of motion:
v^2 = u^2 + 2as
=> v^2 = 0 + 2 × 9.8 m/s^2 × s (where s is the
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A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer?
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A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer?.
A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer?.
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A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer?, a detailed solution for A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer? has been provided alongside types of A rocket, with an initial mass of 3000kg, is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 40 kg per deeond. The burnt watter is ejected vertically downwards with a speed of 4000 m/see relative to the rocket. If burning stops after one minute. Find the maximum velocity of rocket.Correct answer is '5837.75'. Can you explain this answer? theory, EduRev gives you an
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