consider a rocket stage operating in "field$-$free space" where the rocket thrust is the only force. If the rocket's effective exhaust velocity is $3,140$ m$/$s and the initial toal vehicle mass is $4,500$ kg$,$ determine the propellant mass required to increase the vehicle's velocity by $2,600$ m$/$s$.$ Also determine the payload ratio if its structural coefficient is $0\mathrm{.}097$ and the desired velocity increment is $2,600$ m$/$s$.$