1. Momentum

The mass of gas emitted from the rear of the toy rocket is initially 0.1 kg/s.If the speed relative to the rocket is 50 m/s, and the mass of the rocket is 2 kg.What is the initial acceleration of the rocket?

2. Re: Momentum

Using conservation of momentum:

$m_gv_g+m_rv_r=0$

Differentiate with respect to time:

$v_g\frac{dm_g}{dt}+m_r\frac{dv_r}{dt}=0$

Now plug in the given values at time $t=0$, then solve for the acceleration of the rocket $a_r=\frac{dv_r}{dt}$.