A particle A A\,A of mass 3 kg and a particle B B\,B of mass 6 kg are connected by a light inextensible string. The string passes over a smooth pulley fixed at the top of a rough inclined plane. The coefficient of friction between the particle A A\,A and the plane is 0.25. The plane is inclined at an angle of α∘ \alpha^\circ\,α∘ to the horizontal such that cosα=0.6\cos \alpha = 0.6cosα=0.6. A A\,A lies on the plane and B B\,B hangs freely from the edge of the plane 1.5 m above the ground with the string taut. The system is released from rest. Assume B B\,B hits the ground before A A\,A reaches the pulley.
Find the speed at which B B\,B hits the ground.
139 exam-style questions on AQA A Level Maths 3.3 R: Forces and Newton's laws, covering 3.3.1 Concept of a force and Newton's first law, 3.3.2 Newton's second law, 3.3.3 Weight and motion under gravity, 3.3.4 Newton's third law and equilibrium, 3.3.5 Addition of forces and resultants (A-level only), and 3.3.6 Friction (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.