Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut’s acceleration is measured to be 0.893 m/s2 . (a) Calculate her mass. (b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut’s acceleration. Propose a method in which recoil of the vehicle is avoided.

a

Her mass is

b

The measurement of the  astronaut acceleration would be defined by relation

Hence it is affected by the mass of the vehicle, the acceleration of the vehicle and her mass

Now to avoid recoil on the vehicle the force on the astronaut should not be provided by the vehicle  

Explanation:

From the question we are told that

            The net external force is  

            The astronaut's acceleration

Generally force is mathematically represented as

Where m is the mass of the astronaut

  Now making m the subject in order to obtain the mass we have

Now when this force is applied it is both felt by the astronaut and the vehicle

Hence

=>        

    This means that the measurement of the  astronaut acceleration would be defined by relation

i don't know that i agree with that but what's the question ?