Question

Ракета массой 400 кг поднялась на высоту 1000м. Определите скорость, с которой вылетели продукты сгорания из ракеты. Считайте что весь запас топлива массой 20 кг сгорел мгновенно.

Answer 1

V1=sqrt(2*g*h)=sqrt(2*10*1000)=141,4 м/с
m1*V1=m2*V2
V2=m1*V1/m2=400*141,4/20=2828 м/с

Answer 2

Calculation of the Velocity of Exhausted Combustion Products

To determine the velocity with which the combustion products were expelled from the rocket, we can use the principle of conservation of momentum. According to this principle, the change in momentum of the rocket is equal and opposite to the change in momentum of the exhausted combustion products.

The momentum of an object is given by the product of its mass and velocity. Therefore, we can calculate the initial momentum of the rocket and the final momentum of the exhausted combustion products and equate them to find the velocity of the products.

Given: - Mass of the rocket (m1) = 400 kg - Height reached by the rocket (h) = 1000 m - Mass of the fuel (m2) = 20 kg

To solve this problem, we need to make some assumptions: - The rocket starts from rest. - The rocket experiences no air resistance. - The entire mass of the fuel is instantaneously converted into exhaust products.

Calculation Steps:

1. Calculate the initial momentum of the rocket (m1) before the fuel is burned: - Initial momentum (p1) = m1 * 0 (assuming the rocket starts from rest) - Initial momentum (p1) = 0

2. Calculate the final momentum of the exhausted combustion products (m2) after the fuel is burned: - Final momentum (p2) = m2 * v2 (where v2 is the velocity of the exhausted combustion products)

3. Equate the initial and final momentum to find the velocity of the exhausted combustion products: - p1 = p2 - 0 = m2 * v2 - v2 = 0

Based on the calculations, the velocity with which the exhausted combustion products left the rocket is 0 m/s. This means that the products were expelled with no velocity relative to the rocket.

Please note that this calculation assumes ideal conditions and neglects factors such as air resistance and the actual dynamics of the rocket's propulsion system.