At the moment of reaching its speed of 200 m / s, the first stage with a mass of 100 tons is separated

At the moment of reaching its speed of 200 m / s, the first stage with a mass of 100 tons is separated from the rocket, and its speed after separation is 50 m / s. In this case, the speed of the second stage increases to 250 m / s. Find the mass of the second stage and the rocket if both stages were moving in the same direction.

Given:

v = 200 m / s – the speed of the rocket before the separation of the stages;

m1 = 100 tons = 100,000 kilograms is the mass of the first stage of the rocket;

v1 = 50 m / s is the speed of the first stage of the rocket after separation;

v2 = 250 m / s is the speed of the second stage of the rocket after separation.

It is required to determine the mass of the second stage m2 (kilogram) and the mass of the rocket m (kilogram).

Since, according to the condition of the problem, both stages moved in the same direction, then according to the law of conservation of momentum:

(m1 + m2) * v = m1 * v1 + m2 * v2;

m1 * v + m2 * v = m1 * v1 + m2 * v2;

m1 * v – m1 * v1 = m2 * v2 – m2 * v;

m1 * (v – v1) = m2 * (v2 – v);

m2 = m1 * (v – v1) / (v2 – v) = 100000 * (200 – 50) / (250 – 200) = 100000 * 150/50 =

= 100,000 * 3 = 300,000 kilograms.

Then the mass of the entire rocket is equal to:

m = m1 + m2 = 100000 + 300000 = 400000 kilograms (400 tons).

Answer: the mass of the second stage is 300 tons, the mass of the entire rocket is 400 tons.