- 383

- 13

**1. Homework Statement**

In two rockets, one of which moves and the other is at rest, the motors are connected for a short time. During their operation they throw the same mass of gas (small in comparison with the mass of the rocket) at the same speed with respect to the rockets. The kinetic energy of the rocket in motion was ##E_0##, increase by 4 percent. Determine the energy of the second rocket

**2. Homework Equations**

##E_k=\frac{1}{2}mv^2##

**3. The Attempt at a Solution**

I first wrote the final kinetic energy of the second rocket: ##E_k=E_0+\frac{4}{100}E_0##, then by using that equation: ##\frac{1}{2}mv_f^2=\frac{1}{2}mv_0^2+\frac{1}{25}(\frac{1}{2}mv_0^2)=mv_f^2=mv_0^2+\frac{1}{25}mv_0^2\Rightarrow m_vf^2=\frac{25mv_0^2+mv_0^2}{25}=\frac{26mv_0^2}{25}\Rightarrow 25v_f^2=26v_0^2##. After that I don't know what to do.