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.
Practise Edexcel A Level Maths Applications of Forces with exam-style questions for A Level Maths. 47 questions covering Static Particles, Modelling with Statics, Friction and Static Particles, Static Rigid Bodies, Dynamics and Inclined Planes, and Connected Particles 2, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.