Let there be two particles of same mass inside an elliptical container placed along  $\frac{x^2}{2}+y^2=1.$  Initially, both particles are at  $\left(1,0\right)$  At $t=0,$   first particles $\left(P_1\right)$  starts moving towards negative x-axis and second particle $\left(P_2\right)$  starts moving along a line at an angle of  $\frac{\pi }{3}$  from positive x-axis, both having speed of  $\sqrt{2}$   units/s. The particles can collide with container and with each other, all collisions being perfectly elastic. Let   $f\left(t\right)$  be a function of distance between the two particles at any time  t,  Let  $g\left(t\right)$  and  $h\left(t\right)$  be function of distance of  $P_1$  and  $P_2$  respectively from  $(1,0)$  at any time  t.