Urcare
[tex] E_i=mv_0^2/2,E_f=mgh=mgd\sin\alpha,L_{F_f}=-\mu mg\cos\alpha\\\\mv_0^2/2-\mu mg\cos\alpha=mgd\sin\alpha\implies v_0^2/2-\mu g\cos\alpha=gd\sin\alpha \\ \\ d=\dfrac{v_0^2/2-\mu g\cos\alpha}{g\sin\alpha}=\dfrac{v_0^2}{2g\sin\alpha}-\mu \text{ctg}\alpha [/tex]
Coborare
[tex] E_i=mgh=mgd\sin\alpha+mv_0^2/2,E_f=0,L_{F_f}=-\mu m g\cos\alpha\\\\ mgd\sin\alpha+mv_0^2/2-\mu mg\cos\alpha=0 \implies \\ \\ d=\dfrac{\mu g\cos\alpha-v_0^2/2}{gsin\alpha}=\mu\text{ctg}\alpha-\dfrac{v_0^2}{2g\sin\alpha} [/tex]
