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A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)?
Verified Answer
A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s wit...
Force on the rocket:
F= v dm/dt
= 12000 x 15= 180000 N
Mass after 1 min
M= m - dm/dt x t
= 5700 - 15 x 60
= 4800 kg
Accelration
a= F/m
or a= F-mg/M
= 180000 - (4800 x 10)/ 4800
=27.5 m/s^2
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A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s wit...
Given information:
Mass of rocket (m) = 5700 kg
Rate of mass ejection (dm/dt) = 15 kg/s
Speed of ejection (v) = 12 km/s = 12,000 m/s
Acceleration due to gravity (g) = 10 m/s²
Calculating the acceleration:
Step 1: Find the initial mass of the rocket.
The initial mass of the rocket can be calculated by subtracting the mass ejected from the total mass of the rocket.
Initial mass of the rocket (m₀) = m - (dm/dt)t where t is the time passed since ejection.
In this case, since we want to calculate the acceleration 1 minute after the blast, t = 1 minute = 60 seconds.
m₀ = 5700 kg - (15 kg/s)(60 s) = 5700 kg - 900 kg = 4800 kg
Step 2: Find the final mass of the rocket.
The final mass of the rocket can be calculated by subtracting the mass ejected from the initial mass of the rocket.
Final mass of the rocket (m₁) = m₀ - (dm/dt)(t + Δt) where Δt is a very small time interval.
In this case, Δt is negligible since the time interval is very small.
m₁ = 4800 kg - (15 kg/s)(60 s) = 4800 kg - 900 kg = 3900 kg
Step 3: Find the change in momentum.
The change in momentum of the rocket can be calculated using the formula Δp = m₁v - m₀v, where v is the speed of ejection.
Δp = (3900 kg)(12,000 m/s) - (4800 kg)(12,000 m/s) = 46,800,000 kg·m/s - 57,600,000 kg·m/s = -10,800,000 kg·m/s
Step 4: Find the net force acting on the rocket.
The net force acting on the rocket can be calculated using the formula F = Δp/Δt, where Δt is a very small time interval.
In this case, Δt is negligible since the time interval is very small.
F = -10,800,000 kg·m/s ÷ Δt
Step 5: Find the acceleration of the rocket.
The acceleration of the rocket can be calculated using the formula F = ma, where F is the net force acting on the rocket and a is the acceleration of the rocket.
a = F/m₁ = (-10,800,000 kg·m/s ÷ Δt) ÷ 3900 kg
Step 6: Substitute the given values to find the acceleration.
a = (-10,800,000 kg·m/s ÷ Δt) ÷ 3900 kg = -2,769.23 m/s²
Step 7: Convert the acceleration to positive value.
Since the acceleration is negative, indicating a decrease in velocity, we convert it to a positive value by taking its magnitude.
Acceleration = |a| = |-2,769.23 m/s²| = 2,769
Mass of rocket (m) = 5700 kg
Rate of mass ejection (dm/dt) = 15 kg/s
Speed of ejection (v) = 12 km/s = 12,000 m/s
Acceleration due to gravity (g) = 10 m/s²
Calculating the acceleration:
Step 1: Find the initial mass of the rocket.
The initial mass of the rocket can be calculated by subtracting the mass ejected from the total mass of the rocket.
Initial mass of the rocket (m₀) = m - (dm/dt)t where t is the time passed since ejection.
In this case, since we want to calculate the acceleration 1 minute after the blast, t = 1 minute = 60 seconds.
m₀ = 5700 kg - (15 kg/s)(60 s) = 5700 kg - 900 kg = 4800 kg
Step 2: Find the final mass of the rocket.
The final mass of the rocket can be calculated by subtracting the mass ejected from the initial mass of the rocket.
Final mass of the rocket (m₁) = m₀ - (dm/dt)(t + Δt) where Δt is a very small time interval.
In this case, Δt is negligible since the time interval is very small.
m₁ = 4800 kg - (15 kg/s)(60 s) = 4800 kg - 900 kg = 3900 kg
Step 3: Find the change in momentum.
The change in momentum of the rocket can be calculated using the formula Δp = m₁v - m₀v, where v is the speed of ejection.
Δp = (3900 kg)(12,000 m/s) - (4800 kg)(12,000 m/s) = 46,800,000 kg·m/s - 57,600,000 kg·m/s = -10,800,000 kg·m/s
Step 4: Find the net force acting on the rocket.
The net force acting on the rocket can be calculated using the formula F = Δp/Δt, where Δt is a very small time interval.
In this case, Δt is negligible since the time interval is very small.
F = -10,800,000 kg·m/s ÷ Δt
Step 5: Find the acceleration of the rocket.
The acceleration of the rocket can be calculated using the formula F = ma, where F is the net force acting on the rocket and a is the acceleration of the rocket.
a = F/m₁ = (-10,800,000 kg·m/s ÷ Δt) ÷ 3900 kg
Step 6: Substitute the given values to find the acceleration.
a = (-10,800,000 kg·m/s ÷ Δt) ÷ 3900 kg = -2,769.23 m/s²
Step 7: Convert the acceleration to positive value.
Since the acceleration is negative, indicating a decrease in velocity, we convert it to a positive value by taking its magnitude.
Acceleration = |a| = |-2,769.23 m/s²| = 2,769
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A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)?
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A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)? 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 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)?.
A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)? 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 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A rocket of mass 5700 kg ejects mass at a constant rate of 15 kg/s with constant speed of 12 km/s. The acceleration of rocket 1 minute after blast is (g=10m/s2)?.
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