Question

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?

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asked 2020-10-27
A rocket is fired in deep space, where gravity is negligible. In the first second it ejects of \(\displaystyle{\frac{{{1}}}{{{160}}}}\) its mass as exhaust gas and has an acceleration of \(\displaystyle{16.0}\ \frac{{m}}{{s}^{{2}}}\).
What is the speed of the exhaust gas relative to the rocket?

Answers (1)

2020-10-28
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, \(\displaystyle{v}={\frac{{{M}{a}}}{{{\frac{{{d}{M}}}{{{\left.{d}{t}\right.}}}}}}}\) this is a little weird, but you are given that at that instant, dM/dt is M/160 per second so \(\displaystyle{v}={M}\cdot{16}\) m/s
\(\displaystyle{\frac{{\frac{{M}}{{160}}}}{{{1}\ {\sec}}}}={2560}\ \frac{{m}}{{s}}\)
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