Two billiard balls with the same mass m move towards one another. Ball one moves in the positive x$-$direction with a speed of v$1$i$,$ and ball two moves in the negative x$-$direction with a speed of v$2$i$.$ The two balls collide elastically, and both balls change direction after the collision.

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If the initial speeds of the balls were v$1$i $=2\mathrm{.}0$ m$/$s and v$2$i $=1\mathrm{.}0$ m$/$s$,$ what would be the final speed and direction of ball two, v$2$f$,$ in meters per second?

v$2$f $=1\mathrm{.}0$ m$/$s$,$ in the negative x$-$direction.v$2$f $=1\mathrm{.}0$ m$/$s$,$ in the positive x$-$direction.v$2$f $=2\mathrm{.}0$ m$/$s$,$ in the negative x$-$direction.v$2$f $=0$ m$/$s$.$v$2$f $=2\mathrm{.}0$ m$/$s$,$ in the positive x$-$direction.