A particle of mass 8 kg is projected with a speed of 5 m s^-1 up a line of greatest slope of a rough plane inclined at an angle α to the horizontal, where sin α = ⁵/₁₃. The motion of the particle is resisted by a constant frictional force of magnitude 15 N. The particle comes to instantaneous rest after travelling a distance x m up the plane.

(i) Express the change in gravitational potential energy of the particle in terms of x.

(ii) Use an energy method to find x.