A particle is moving with kinetic Energy E, straight up an inclined plane with an angle  α,  the coefficient of friction being  μ.   The work done against friction before the particle comes to rest is,

given KE=E  is utilized in work done in overcoming friction and climbing up the incline apply principle of conservation of energy KE=workfriction+PE E=f.s+mgssinα here f =μmgcosα =force of friction; s is displacement up the incline plane E=(μmgcosα).s +mgssinα s=Emg(μcosα+sinα) work done against friction =f.s=(μmgcosα).Emg(μcosα+sinα) work done against friction =μEcosα(μcosα+sinα)