A rocket is fired in deep space, where gravity is negligible. In the first second it ejects of \frac{1}{160} its mass as exhaust gas and has an acceleration of 16.0\ m/s^2. What is the speed of the exhaust gas relative to the rocket?

Cabiolab

Cabiolab

Answered question

2020-10-27

A rocket is fired in deep space, where gravity is negligible. In the first second it ejects of 1160 its mass as exhaust gas and has an acceleration of 16.0 ms2
What is the speed of the exhaust gas relative to the rocket?

Answer & Explanation

Layton

Layton

Skilled2020-10-28Added 89 answers

If you look at the derivation for thrust from a rocket, theend result is:
Ma=vdM/dt
Where M is the mass of the rocket, a is the acc of the rocket,and v is the speed of the exhaust gas relative to the rocket.
So, v=MadMdt this is a little weird, but you are given that at that instant, dM/dt is M/160 per second so v=M16 m/s
M1601 sec=2560 ms

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