A rocket of mass 5700 ,kg ejects mass at a co | vedclass

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(B) The thrust force on the rocket is given by $F_{thrust} = v_{rel} \left( \frac{dm}{dt} \right)$.Given: Initial mass $M_0 = 5700 \,kg$,rate of mass

Vedclass · Accepted Answer

$27.5$

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(B) The thrust force on the rocket is given by $F_{thrust} = v_{rel} \left( \frac{dm}{dt} ight)$.Given: Initial mass $M_0 = 5700 \,kg$,rate of mass ejection $\frac{dm}{dt} = 15 \,kg/s$,relative speed $v = 12 \,km/s = 12000 \,m/s$,and $g = 10 \,m/s^2$.After $t = 60 \,s$ ($1$ minute),the mass of the rocket is $m = M_0 - \left( \frac{dm}{dt} ight) t = 5700 - (15 	imes 60) = 5700 - 900 = 4800 \,kg$.The net force acting on the rocket is $F_{net} = F_{thrust} - mg = v \left( \frac{dm}{dt} ight) - mg$.The acceleration $a$ is given by $a = \frac{F_{net}}{m} = \frac{v \left( \frac{dm}{dt} ight)}{m} - g$.Substituting the values: $a = \frac{12000 	imes 15}{4800} - 10$.$a = \frac{180000}{4800} - 10 = 37.5 - 10 = 27.5 \,m/s^2$.

$A$ rocket of mass $5700 \,kg$ ejects mass at a constant rate of $15 \,kg/s$ with a constant speed of $12 \,km/s$. The acceleration of the rocket $1 \,minute$ after the blast is ........... $m/s^2$ $(g=10 \,m/s^2)$.

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