A SpaceX rocket experiences a malfunction and explodes into three pieces. The tail section of the rocket with a mass of $5\mathrm{.}0{10}^{5}kg$ is ejected backwards at $2\mathrm{.}0{10}^5\frac{m}{s}.$ Another section with mass $8\mathrm{.}0{10}^{5}kg$ flies forward at $1\mathrm{.}0{10}^6\frac{m}{s}.$ The mass of the rocket is $2\mathrm{.}0{10}^{6}kg$ and its initial speed is $5\mathrm{.}0{10}^6\frac{m}{s}$ to the left. What is the speed and direction of the other piece of the rocket?