Question

A rocket is fired in deep space, where gravity is negligible. In the first second it ejects 1/160 of its mass as exhaust gas and has an acceleration of 14.0 m/s^2.
Required:
What is the speed vgas of the exhaust gas relative to the rocket?

Answer 1

Answer:

840 m/s

Explanation:

Given that,

In the first second the rocket ejects 1/160 of its mass as exhaust gas and has an acceleration of 14.0 m/s².

We need to find the speed of the exhaust gas relative to the rocket.

The thrust of rocket is given by :

$T=v_{gas}\dfrac{dm}{dt}\\\\ma=v_{gas}\dfrac{dm}{dt}\\\\v_{gas}=\dfrac{ma}{\dfrac{dm}{dt}}\\\\v_{gas}=\dfrac{14m}{\dfrac{1}{60}m}\\\\v_{gas}=840\ m/s$

So, the speed of the exhaust gas relative to the rocket is 840 m/s.