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Answer :
The burnout velocity of the booster is approximately 5,964 m/s.
To calculate the burnout velocity of the booster, we need to consider the rocket equation, which relates the mass ratio of the rocket and the specific impulse (Isp) of the propellant.
The rocket equation is expressed as:
Δv = Isp * g0 * ln(m0/mf)
Where:
Δv is the change in velocity (burnout velocity)
Isp is the specific impulse of the propellant
g0 is the standard acceleration due to gravity (approximately 9.81 m/s^2)
m0 is the initial mass of the rocket (propellant mass + structure mass + payload mass)
mf is the final mass of the rocket (propellant mass + structure mass)
Payload mass = 50 kg
Propellant mass = 5,500 kg
Structure mass = 450 kg
Isp = 325
We can calculate the initial mass (m0) by adding the payload mass, propellant mass, and structure mass:
m0 = 50 kg + 5,500 kg + 450 kg = 6,000 kg
Next, we calculate the final mass (mf) by adding the propellant mass and structure mass:
mf = 5,500 kg + 450 kg = 5,950 kg
Plugging these values into the rocket equation, we have:
Δv = 325 * 9.81 m/s^2 * ln(6,000 kg / 5,950 kg)
Evaluating this expression gives us a burnout velocity of approximately 5,964 m/s.
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