A rocket weighing 1000 tons is launched vertically upward under the action of engines emitting gases at a speed of 4 km / s

A rocket weighing 1000 tons is launched vertically upward under the action of engines emitting gases at a speed of 4 km / s, a fuel consumption of 3250 kg / s. with what acceleration does the rocket start its upward motion?

mр = 1000 t = 1,000,000 kg.
mt = 3250 kg.
Vt = 4 km / s = 4000 m / s.
а- ?
t = 1 s.
According to the law of conservation of momentum: the total momentum of a closed system remains unchanged.
The momentum of the body P is the product of body mass m by its speed V: P = m * V.
(mr – mt) * Vr = mt * Vt.
Vr = mt * Vt / (mr – mt).
The acceleration of the rocket a is determined by the formula: a = (Vр – Vр0) / t.
Since Vр0 = 0, then a = Vр / t.
a = mt * Vt / (mr – mt) * t.
a = 3250 kg * 4000 m / s / (1,000,000 kg – 3250 kg) * 1 s = 13 m / s ^ 2.
Answer: the acceleration of the rocket at launch is a = 13 m / s ^ 2.