A 5000, kg rocket is set for vertical firing. | vedclass

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(B) The thrust force $F$ required to lift the rocket with an upward acceleration $a$ is given by the equation: $F = v_{ex} \cdot \frac{dm}{dt} = m(g +

Vedclass · Accepted Answer

$187$

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(B) The thrust force $F$ required to lift the rocket with an upward acceleration $a$ is given by the equation: $F = v_{ex} \cdot \frac{dm}{dt} = m(g + a)$.Here,$m = 5000\, kg$ is the mass of the rocket,$g = 10\, m/s^2$ is the acceleration due to gravity,$a = 20\, m/s^2$ is the required upward acceleration,and $v_{ex} = 800\, m/s$ is the exhaust speed.Rearranging the formula to solve for the rate of mass ejection $\frac{dm}{dt}$:$\frac{dm}{dt} = \frac{m(g + a)}{v_{ex}}$Substituting the given values:$\frac{dm}{dt} = \frac{5000 	imes (10 + 20)}{800}$$\frac{dm}{dt} = \frac{5000 	imes 30}{800} = \frac{150000}{800} = 187.5\, kg/s$.Thus,the amount of gas ejected per second is $187.5\, kg/s$.

$A$ $5000\, kg$ rocket is set for vertical firing. The exhaust speed is $800\, m/s$. To give an initial upward acceleration of $20\, m/s^2$,the amount of gas ejected per second to supply the needed thrust will be ........... $kg/s$ $(g = 10\, m/s^2)$. (in $.5$)

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