Question

Рассчитайте скорость, которую будет иметь ракета, стартовая масса которой 1 т, если в результате горения топлива выброшено 200 кг газов со скоростью 2 км/с.

Answer 1

 0=m1*v1+m2*v2
m1*v1=m2*v2
v2=m1*v1/m2=(200 кг*2000 м/с)/1000 кг=400 м/с

Answer 2

Calculating Rocket Speed

To calculate the speed of the rocket, we can use the principle of conservation of momentum. The rocket's initial mass is 1 ton (1000 kg), and 200 kg of gas is expelled with a speed of 2 km/s. We can use the formula:

Final velocity = Initial velocity + (Gas speed * ln(initial mass/final mass))

Using this formula, we can calculate the final velocity of the rocket.

Calculation

The initial mass of the rocket is 1000 kg, and the final mass after the expulsion of 200 kg of gas is 800 kg. The speed of the expelled gas is 2 km/s.

Final velocity = 0 + (2 * ln(1000/800))

Final velocity ≈ 0 + (2 * ln(1.25))

Final velocity ≈ 0 + (2 * 0.22314)

Final velocity ≈ 0 + 0.44628

Final velocity ≈ 0.44628 km/s

Therefore, the speed of the rocket after the expulsion of 200 kg of gas with a speed of 2 km/s is approximately 0.44628 km/s.

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