Question

How much of a single-stage rocket that is 100,000 kg can be anything but fuel if the rocket is to have a final speed of 8.00km/s, given that it expels gases at an exhaust velocity of 2.20×10³ m/s?

Answer 1

To determine the amount of a single-stage rocket that can be anything but fuel, we need to use the principle of conservation of momentum and solve an equation. By equating the initial and final momentum of the rocket, we can find the amount of fuel needed.

Step-by-step explanation:

To calculate how much of a single-stage rocket can be anything but fuel, we need to use the principle of conservation of momentum. The initial momentum of the rocket is given by the product of its mass and initial velocity, which is 100,000 kg multiplied by 0 m/s since the rocket is at rest initially. The final momentum of the rocket is given by the product of its final mass (mass of rocket minus fuel) and final velocity, which is (100,000 - amount of fuel) kg multiplied by 8.00 km/s converted to m/s. Since the exhaust gases are expelled with an exhaust velocity of 2.20 × 10³ m/s, we can equate the initial and final momentum and solve for the amount of fuel.

Using the equation for momentum:

(100,000 kg)(0 m/s) = (100,000 - amount of fuel kg)(8.00 × 10⁳ m/s) + (amount of fuel kg)(2.20 × 10³ m/s)

Simplifying and solving for the amount of fuel, we can find the answer.