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