A small block starts slipping down from a point B on an inclined plane AB, which is making an angle $$\theta $$ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction $$\mu $$. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC, the coefficient of friction is given by $$\mu $$ = ktan $$\theta $$ . The value of k is _________.

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), the kinetic energy of the particle (in )) is :
(Figure drawn is schematic and not to scale; take g = 10 ms^-2)