A solid billiard ball with a mass of $230$g and a radius of $4\mathrm{.}00$ cm is rolling across a flat surface with a speed of $1\mathrm{.}35$ m$/$s$.$ It encounters an incline at a $200$ with respect to the horizontal. How far up the incline does the ball roll before it stops?

Answer this question using the principle of energy conservation. Use g$=10$ m$/$s$2$for the acceleration due to gravity.