I have a question where two particles collide with each other in a non central way.
Mass of particle 1 ($m_1$) is $1\text{kg}$ and its velocity $v_1$ is $5\text{m/s}$ (moving along the x-axis) before it collides with particle 2 (which isn't moving). After the collision, the particle 1 will have a momentum of $2\text{kg.m/s}$ in the x axis ($P_{1x} = 2\text{kg.m/s}$) and a momentum of $-3\text{kg.m/s}$ in y axis ($P_{1y} = -3\text{kg.m/s}$).
I am asked to find the kinetic energy of particle 2 after the collision.
I know that kinetic energy is conserved in elastic collisions and thus; $$\frac{1}{2} m_1(v_{1i})^2 + \frac{1}{2} m_2(v_{2i})^2 = \frac{1}{2} m_1(v_{1f})^2 + \frac{1}{2} m_2 (v_{2f})^2$$
But I am confused when it comes to working in two dimensions $(x,y)$. Can you please help me about this by maybe providing with some equations or a helpful link?