A 6000 ,kg rocket is set for firing. If the e | vedclass

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(D) The thrust force $F$ produced by the rocket engine is given by the formula $F = v_{e} \left( \frac{dm}{dt} \right)$,where $v_{e}$ is the exhaust s

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$60$

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(D) The thrust force $F$ produced by the rocket engine is given by the formula $F = v_{e} \left( \frac{dm}{dt} ight)$,where $v_{e}$ is the exhaust speed and $\frac{dm}{dt}$ is the rate of mass ejection.To overcome the weight of the rocket,the thrust must be equal to the gravitational force acting on the rocket,so $F = mg$.Given: Mass of the rocket $m = 6000 \,kg$,acceleration due to gravity $g \approx 10 \,m/s^2$,and exhaust speed $v_{e} = 1000 \,m/s$.Equating the forces: $v_{e} \left( \frac{dm}{dt} ight) = mg$.Substituting the values: $1000 	imes \left( \frac{dm}{dt} ight) = 6000 	imes 10$.$1000 	imes \left( \frac{dm}{dt} ight) = 60000$.$\frac{dm}{dt} = \frac{60000}{1000} = 60 \,kg/s$.Therefore,the amount of gas that must be ejected each second is $60 \,kg$.

$A$ $6000 \,kg$ rocket is set for firing. If the exhaust speed is $1000 \,m/s$,how much gas must be ejected each second to supply the thrust needed to overcome the weight of the rocket?

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