Write a Python code that simulates this process using an Euler step with a time step dt $=0\mathrm{.}02$ to update the position vectors

given by equation $(1).$ Make sure that the interaction between the balls and the walls as well as between each other is correct.

You may want to set up clear simple examples where you check that those are indeed correct $($justify your choices$).$ Then, take

a pool table with dimensions $[0,1]\backslash$times $[0,1].$ The radius of both billiards balls is r $=\mathrm{.}05.$ The initial velocity vector is $(\mathrm{.}1,\mathrm{.}5)$

for the red ball and $(\mathrm{.}11,\mathrm{.}2)$ for the blue one. The original positions are $(\mathrm{.}75,5$r$)$ for the red ball and $(\mathrm{.}25,5\mathrm{.}5$r$)$ for the blue

one. Take $\backslash$alpha $=\mathrm{.}8$ and $\backslash$beta $=\mathrm{.}98.$ Run the simulation from t $=0$ to tfinal $=50$ and display the balls$$ motion.