Question

A spacecraft called deep space 1, mass $486kg$ uses an ion drive engine. This kind of engine is made to be used in deep space. Perform a calculation to comment on the prediction made in this statement.
The ion propulsion on deep space 1 expels $0.13kg$ if xenon propellant each day. The xenon are expelled from the spacecraft at a speed of $30km{{s}^{-1}}$. The speed of the aircraft is predicted to initially increase by about $8m{{s}^{-1}}$ each day.

Answer 1

Hint: It has been mentioned in the question that an external force has been applied to the spacecraft. The conservation of linear momentum is to be applied here. And find the velocity of the spacecraft. These all will help you in solving questions.

Complete step by step answer:
Some kind of external force has been applied to the spacecraft in order to expel the xenon from it. According to the conservation of linear momentum,
${{m}_{1}}{{v}_{1}}={{m}_{2}}{{v}_{2}}$
The initial momentum of the body will be equivalent to the final momentum of the body.
Here we can see that the mass of xenon expelled from spacecraft can be written as,
${{m}_{X}}=0.13kg$
The velocity with which xenon get expelled is given as,
${{v}_{X}}=30km{{s}^{-1}}$
The mass of the spacecraft is mentioned as,
$M=486kg$
The mass of the spacecraft after the expulsion of the xenon will be,
${{m}_{s}}=M-{{m}_{X}}=486-0.13=485.57kg$
Therefore applying the conditions mentioned in the question for conservation of linear momentum will give,
${{m}_{X}}{{v}_{X}}={{m}_{s}}{{v}_{s}}$
Substituting the values given in the question in this equation will give,
$0.13\times 30=485.57\times {{v}_{s}}$
Rearranging the equation will give,
$\dfrac{0.13\times 30}{485.57}={{v}_{s}}$
Simplifying the equation will give,
${{v}_{s}}=8.02m{{s}^{-1}}$
That is the speed of the aircraft is found to initially increase by about $8m{{s}^{-1}}$each day. Therefore the prediction mentioned in the question is correct.

Note: Conservation of linear momentum is a general law in physics. The quantity called as the momentum that represents the motion will not change in an isolated collection of objects, according to this law. That means, the total momentum of a system will remain constant.