How to Figuring out the coefficient of kinetic friction?

Question

A small block slide 20 cm along a frictionless triangular ramp. The surface of the ramp makes an angle of 30 degrees above the level table top on which it is mounted. When the block reaches the end of the ramp it slides 30 cm before coming to rest. What is the codefficient of kinetic friction on the table top?

Answer 1

The block slides 20 cm on the ramp inclined at 30 degrees, means it has fallen to a distance h =  20 sin (30) = 10 cm.

velocity gained ( g = 10 m/s^2) = sqrt ( 2gh )

                                                      

It stopped by a distance of 30 cm

u^2 = 2as

a = 2gh / 2s

   =  gh/s

coeff of fric = ma/mg = a/g

                    = h/s

                    = .33  ( h = 10 cm and s = 30 cm )