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A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/s^2?
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A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with ...
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A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with ...
Given:
Mass of the rocket (m) = 5700 kg
Rate of mass ejection (dm/dt) = 15 kg/s
Speed of ejection (v) = 12 km/s = 12000 m/s
To find:
Acceleration of the rocket (a) 1 minute after the blast
Formula:
The rocket equation is given by:
F = (dm/dt) * v
The force acting on the rocket (F) is equal to the rate of change of momentum of the rocket.
The acceleration (a) of the rocket can be calculated using Newton's second law:
F = ma
Calculation:
Step 1: Calculate the force acting on the rocket
F = (dm/dt) * v
F = 15 kg/s * 12000 m/s
F = 180000 N
Step 2: Calculate the acceleration of the rocket
F = ma
180000 = 5700 * a
a = 180000 / 5700
a ≈ 31.579 m/s²
However, this value is the acceleration immediately after the blast. We need to calculate the acceleration 1 minute after the blast.
Step 3: Convert 1 minute to seconds
1 minute = 60 seconds
Step 4: Calculate the change in mass after 1 minute
Change in mass (Δm) = (dm/dt) * Δt
Δm = 15 kg/s * 60 s
Δm = 900 kg
Step 5: Calculate the new mass of the rocket after 1 minute
New mass (m') = m - Δm
m' = 5700 kg - 900 kg
m' = 4800 kg
Step 6: Calculate the new acceleration after 1 minute
F' = (dm/dt) * v
F' = 15 kg/s * 12000 m/s
F' = 180000 N
F' = m' * a'
180000 = 4800 kg * a'
a' = 180000 / 4800
a' ≈ 37.5 m/s²
Therefore, the acceleration of the rocket 1 minute after the blast is approximately 37.5 m/s², which is closest to option a) 34.9 m/s².
Mass of the rocket (m) = 5700 kg
Rate of mass ejection (dm/dt) = 15 kg/s
Speed of ejection (v) = 12 km/s = 12000 m/s
To find:
Acceleration of the rocket (a) 1 minute after the blast
Formula:
The rocket equation is given by:
F = (dm/dt) * v
The force acting on the rocket (F) is equal to the rate of change of momentum of the rocket.
The acceleration (a) of the rocket can be calculated using Newton's second law:
F = ma
Calculation:
Step 1: Calculate the force acting on the rocket
F = (dm/dt) * v
F = 15 kg/s * 12000 m/s
F = 180000 N
Step 2: Calculate the acceleration of the rocket
F = ma
180000 = 5700 * a
a = 180000 / 5700
a ≈ 31.579 m/s²
However, this value is the acceleration immediately after the blast. We need to calculate the acceleration 1 minute after the blast.
Step 3: Convert 1 minute to seconds
1 minute = 60 seconds
Step 4: Calculate the change in mass after 1 minute
Change in mass (Δm) = (dm/dt) * Δt
Δm = 15 kg/s * 60 s
Δm = 900 kg
Step 5: Calculate the new mass of the rocket after 1 minute
New mass (m') = m - Δm
m' = 5700 kg - 900 kg
m' = 4800 kg
Step 6: Calculate the new acceleration after 1 minute
F' = (dm/dt) * v
F' = 15 kg/s * 12000 m/s
F' = 180000 N
F' = m' * a'
180000 = 4800 kg * a'
a' = 180000 / 4800
a' ≈ 37.5 m/s²
Therefore, the acceleration of the rocket 1 minute after the blast is approximately 37.5 m/s², which is closest to option a) 34.9 m/s².
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A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/s^2?
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A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/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 mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/s^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/s^2?.
A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/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 mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/s^2? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of mass 5700kg ejects mass at a constant rate of 15kg/s with constant speed of 12km/s. The acceleration of the rocket 1 min after the blast is (g=10m/s^2) a) 34.9 m/s^2 b) 27.5 m/s^2 c) 3.50 m/s^2 d) 13.5 m/s^2?.
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