Need help In Rocket Physics (1)

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Fuel is ejected from a rocket of mass ${ M }_{ 0 }$ at a velocity $u$ $m/s$ relative to Rocket. Fuel is ejecting at constant rate of $\mu \quad Kg/s$ . Initial Velocity rocket starts from rest from the surface of earth

( Neglect air and other resistance force in both Cases)

Q1). Assume gravity is constant , Find acceleration, velocity and Thrust as a function of time.

Q2). Assume gravity changes with height $h$ from earth surface as $g\left( h \right) =\frac { g }{ { \left( 1+\frac { h }{ { R }_{ e } } \right) }^{ 2 } }$ , Find acceleration, Velocity and Thrust as a function of time.

#Mechanics

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Comments

Is acceleration $\frac{\mu u}{M_{0} -\mu t}$ ?

Harsh Shrivastava - 5 years, 2 months ago

How do you find it ?? I don't know the answer.

Rishabh Deep Singh - 5 years, 2 months ago

Use conservation of momentum and a=dv/dt.

Harsh Shrivastava - 5 years, 2 months ago

@Harsh Shrivastava – You are totally wrong.

We can't apply conservation of momentum as there is gravity and also mass is changing with Time.

Rishabh Deep Singh - 5 years, 2 months ago

Use impulse momentum theoerem in both cases Consider any arbitrary moment in time t and distance y from surface of earth Let us consider that rocket as my system with mass at that point in spacetime as m In time dt let dm mass be ejected absolute velocity of dm is u-v where u is the relative velocity and v is the absolute velocity of rocket at that moment Impulse due to weight is mgdt which is the change in momentum of the system that is rocket After this we form a differentia equation which is dificult to solve in case 2 I am not able to solve the equation In case 1 V= uln(m■\m) -g\p(m■-m) Where m■ is initia mass p is dm\dt

Akash Yadav - 4 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$