A bicycle has a front chainwheel of radius 0.12 m, a rear sprocket of radius 0.045 m and a wheel of radius 0.34 m. The chain does not slip and the rear sprocket turns through the same angle as the wheel.
The pedals turn the front chainwheel through 16π 16\pi\,16π radians. Find the length of chain that passes over the front chainwheel.
Find the angle through which the rear sprocket turns.
Hence find the distance travelled by the bicycle.
State one modelling assumption, other than the chain not slipping, used in your calculation.
In this question you must show detailed reasoning.
317 exam-style questions on OCR A Level Maths 1.5 Trigonometry, covering 1.5.1 Definitions for all arguments, 1.5.2 Sine and cosine rules, 1.5.3 Area of a triangle, 1.5.4 Radian measure (A-level only), 1.5.5 Small angle approximations (A-level only), 1.5.6 Graphs of basic trigonometric functions, 1.5.7 Exact values in radians (A-level only), 1.5.8 Reciprocal and inverse trigonometric ratios (A-level only), 1.5.9 Graphs of reciprocal and inverse functions (A-level only), 1.5.10 Trigonometric identities, 1.5.11 Further trigonometric identities (A-level only), 1.5.12 Double angle and compound angle formulae (A-level only), 1.5.13 Geometrical proofs of formulae (A-level only), 1.5.14 Harmonic form Rcos / Rsin (A-level only), 1.5.15 Trigonometric equations, 1.5.16 Proof involving trigonometric functions (A-level only), and 1.5.17 Trigonometric functions in context. Each one has a worked solution and a mark scheme showing where the marks go.