A perfectly elastic collision takes place between two objects X and Y. The mass of X is $m$ and the mass of Y is $4m$. Before the collision, object X moves with speed $v$, and after the collision it moves in the opposite direction with speed $\frac{3v}{5}$. Object Y is at rest before the collision. Determine the kinetic energy of Y after the collision?
- A$\frac{8}{10}mv^2$
- B$\frac{34}{50}mv^2$
- C$\frac{16}{50}mv^2$
- D$\frac{1}{5}mv^2$