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 15.1 m/s^2.What is the speed v_gas of the exhaust gas relative to the rocket?

Answer 1

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 15.1 m/s^2.What is the speed v_gas of the exhaust gas relative to the rocket?

By means of the rocket equation,

deltaV = cln(Wo/Wt) where
deltaV or dV = the incremental change in velocity over a given time period, Wo = the initial weight at ignition, Wt = the weight after a specific time period and c = the velocity of the exhaust gases. ln = the natural logarithm of.

After one second of firing, the rocket achieves a speed of 15.m/s.

Therefore,
dV = 15.1 = cln[Wo/(Wo-Wo/160)
...= ]5.1 = cln[1/(1-1/160] = ............cln(1.006289)

15.1 = cln(1.006289) - c(.0062696


Hence, c = 2408m/s