Two blocks X X\,X and YYY, of mass 2 kg and 4 kg respectively, are connected by a light inextensible string. The string passes over a smooth pulley at the peak of a rough inclined roof. The roof is inclined at an angle β \beta\,β where cosβ=1213\displaystyle \cos \beta = \frac{12}{13}cosβ=1312. Block X X\,X is on the roof and Y Y\,Y hangs vertically at a height of 2.5 m above the ground. The coefficient of friction between X X\,X and the roof is 0.1. The system is released from rest. Given that Y Y\,Y hits the ground before X X\,X reaches the pulley.
Find the speed of block Y Y\,Y at the instant it 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.