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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$187$

Vedclass · Answer

(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 $.5$)

Similar Questions

$A$ rifle of $20 \,kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} \,kg$ and its final velocity is $400 \,ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $\,N$)?

Is the formula $\vec{F} = m\vec{a}$ valid in all circumstances? Why?

$A$ rocket with a lift-off mass $2 \times 10^4\,kg$ is blasted upwards with an initial acceleration of $5\,m\,s^{-2}$. The initial thrust of the blast is (Take $g = 10\,m\,s^{-2}$).

$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. What is the acceleration of the rocket $50 \ s$ after the launch,neglecting gravity (in $m/s^2$)?

$A$ cracker rocket is ejecting gases at a rate of $0.05 \,kg/s$ with a velocity of $400 \,m/s$. The accelerating force on the rocket is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module