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?

The speed ( Vgas) of the exhaust gas relative to rocket is : 840 m/s

Given data :

In first round Rocket ejects  1/60 of mass as exhaust gas

Acceleration of rocket ( a ) = 14.0 m/s²

Determine the speed of the exhaust gas relative to rocket

We will apply the equation for Rocket thrust

T = Vgas *

where : T = ma

∴ Vgas = ma /

            = 14 m / m

therefore V gas = 840 m/s

Hence we can conclude that the  speed ( Vgas) of the exhaust gas relative to rocket is : 840 m/s

Learn more about Rocket thrust : link

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 :

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