3 A particle of mass 8 kg is projected with a speed of \(5 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) up a line of greatest slope of a rough plane inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 5 } { 13 }\). 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 \(x \mathrm {~m}\) up the plane.

1. Express the change in gravitational potential energy of the particle in terms of \(x\).
2. Use an energy method to find \(x\).