Respuesta :
Answer:4298.8 km/h
Explanation:
Given
velocity of space vehicle [tex]v_i=4350\ km/h[/tex]
Mass of motor is 4 times the mass of module
suppose m is the mass of module therefore
mass of motor is 4 m
velocity of disengaged motor is 64 km/h relative to command module
we can write
[tex]v_{me}=v_{mc}+v_{ce}[/tex]
where [tex]v_{me}[/tex]=velocity of motor relative to earth
[tex]v_{mc}[/tex]=velocity of motor relative to command module
[tex]v_{ce}[/tex]=velocity of command relative to earth
Conserving momentum
[tex]M(v_i)=4m(v_{me})+mv_{ce}[/tex]
where M is combined mass of motor and module
[tex]Mv_i=4m(v_{mc}+v_{ce})+mv_{ce}[/tex]
[tex]5mv_i=4mv_{mc}+4mv_{ce}+mv_{ce}[/tex]
[tex]5mv_i=4mv_{mc}+5mv_{ce}[/tex]
[tex]v_{ce}=v_i-\frac{4}{5}\times v_{mc}[/tex]
[tex]v_{ce}=4350-\frac{4}{5}\times 64[/tex]
[tex]v_{ce}=4350-51.2[/tex]
[tex]v_{ce}=4298.8\ km/h[/tex]
