A crate of weight \(W\text{ N}\) is at rest on rough horizontal ground. The crate is pulled at a constant acceleration of \(1.5\text{ m s}^{-2}\) along the ground in a straight line by a light rope. The rope is inclined at an angle of \(\theta\) to the horizontal, where \(\theta=\sin^{-1}\frac5{13}\). The tension in the rope is \(26\text{ N}\) (see diagram). The coefficient of friction between the crate and the ground is \(0.25\).

(a) Find the value of \(W\).

(b) When the crate reaches a point \(A\), the rope is removed. The speed of the crate at \(A\) is \(8\text{ m s}^{-1}\).

The crate comes to rest at a point \(B\).

Find the distance \(AB\).