# The mass of the missile on the Katyusha installation is 42.5 kg, and the speed is 355 m / s. The duration

The mass of the missile on the Katyusha installation is 42.5 kg, and the speed is 355 m / s. The duration of the combustion of gunpowder in the projectile is 0.7 s. Assuming that the gunpowder burns out instantly, and the exhaust velocity of the combustion products is 2.0 km / s, determine the mass of the powder charge.

mс = 42.5 kg.

Vs = 355 m / s.

t = 0.7 s.

Vg = 2 km / s = 2000 m / s.

mg -?

Since, according to the condition of the problem, the gunpowder in the projectile burns up instantly, the impulse of the gas release Pg is equal to the impulse of the projectile Pc: Pg = Pc. When a rocket is fired, the law of conservation of momentum is valid: mc * Vc = mg * Vg.

The mass of powder combustion products mg will be determined by the formula: mg = mc * Vc / Vg.

mg = 42.5 kg * 355 m / s / 2000 m / s = 7.5 kg.

Answer: during the combustion of gunpowder when fired in a Katyusha rocket launcher, combustion products mg = 7.5 kg are formed.

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