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.
49 exam-style questions on OCR (MEI) A Level Maths 3.5 Newton's Laws of Motion, covering 3.5.1 Meaning of Newton's three laws, 3.5.2 Equation of motion, 3.5.3 Equation of motion for a particle in a straight line, 3.5.4 Model a system of connected particles, 3.5.5 Equations of motion for individual particles, 3.5.6 System with no relative motion as a single particle, and 3.5.7 Equation of motion in a straight line or plane (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.