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lana66690
1 month ago
5

A rocket in deep space has an exhaust-gas speed of 2000 m/s. When the rocket is fully loaded, the mass of the fuel is five times

the mass of the empty rocket. Part A What is the rocket's speed when half the fuel has been burned?
Physics
1 answer:
Sav [3.1K]1 month ago
3 0

Answer:

 v_{f} = 1,386 m / s

Explanation:

The mechanism behind rocket propulsion is defined by the formula

       v_{f} - v₀ =  v_{r} ln (M₀ / Mf)

Here, v refers to the initial, final, and relative velocities, while M indicates the masses

The provided values include the relative velocity (see = 2000 m / s) and the initial mass, where the mass of the rocket when loaded is represented as (M₀ = 5Mf)

For our analysis, we assume the rocket begins at rest (v₀ = 0)

Once half of the fuel has burnt, the mass ratio indicates that the current mass is    

       M = 2.5 Mf

       v_{f} - 0 = 2000 ln (5Mf / 2.5 Mf) = 2000 ln 2

       v_{f} = 1,386 m / s

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