A rocket of initial mass 6000 kg ejects gase | vedclass

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(D) Given: Initial mass $m_0 = 6000 \ kg$,rate of mass ejection $\frac{dm}{dt} = 16 \ kg/s$,relative velocity $V_{rel} = 11 \ km/s = 11000 \ m/s$.Time

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$35$

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(D) Given: Initial mass $m_0 = 6000 \ kg$,rate of mass ejection $\frac{dm}{dt} = 16 \ kg/s$,relative velocity $V_{rel} = 11 \ km/s = 11000 \ m/s$.Time elapsed $\Delta t = 1 \ min = 60 \ s$.The mass of the rocket after $60 \ s$ is $m = m_0 - (\frac{dm}{dt}) \Delta t$.$m = 6000 - (16 	imes 60) = 6000 - 960 = 5040 \ kg$.The thrust force on the rocket is $F = V_{rel} \frac{dm}{dt}$.Using Newton's second law,$F = ma$,so $a = \frac{V_{rel}}{m} \frac{dm}{dt}$.$a = \frac{11000 	imes 16}{5040} = \frac{176000}{5040} \approx 34.92 \ m/s^2$.Rounding to the nearest integer,the acceleration is $35 \ m/s^2$.

$A$ rocket of initial mass $6000 \ kg$ ejects gases at a constant rate of $16 \ kg/s$ with a constant relative speed of $11 \ km/s$ in gravity-free space. What is the acceleration of the rocket $1 \ min$ after the blast? (in $m/s^2$)

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