(i) A uniform ladder of length L and weight w rests against a vertical wall and makes an angle `theta` with the horizontal ground. If the coefficient of friction at the point of contact of the ladder with the wall and ground is `mu`, show that the greatest height x, measured along the ladder from the foot to which a man of weight w may climb without the ladder slipping is given by
`(x)/(L) = (mu(W+w))/(W(1+mu^(2))) (mu +tan theta) - (w)/(2W)`
(ii) If the wall be smooth and coefficient of friction between ladder and ground be 0.25, show that
`x = (L)/(4) (1-(w)/(W)) tan theta - (wL)/(2W)`