Problem $6.$ A $0\mathrm{.}30-$kg puck, initially at rest on a frictionless horizontal surface, is struck by a $0\mathrm{.}20-$kg puck that is initially with a velocity of $2\mathrm{.}0$ m$.$ After the collision, the$0\mathrm{.}20-$kg puck has a speed of $1\mathrm{.}0$ m at an angle of $0=53$ to the original line of motion.$($a$)$ Determine the velocity of the $0\mathrm{.}30$ kg puck after the collision.$($b$)$ Is the collision an elastic one? Prove it$.$