An aerodynamic profile for a glider wing is designed to be symmetric about the chord line (the xxx-axis). The upper boundary of the wing's cross-section is modelled by the parametric equations:
x=−1.5t2 x = -1.5t^2 x=−1.5t2 y=15t−0.75t2 y = 15t - 0.75t^2 y=15t−0.75t2for 0≤t≤200 \le t \le 200≤t≤20, where xxx and yyy are measured in millimetres.
Determine the total length of the glider wing along the xxx-axis.
Obtain an expression for dydx\frac{dy}{dx}dxdy in terms of ttt.
Hence, prove that the maximum thickness (total width) of the wing is exactly one-quarter of its total length.
Practise Edexcel A Level Maths Differentiation with exam-style questions for A Level Maths. 311 questions covering 9.1 Differentiating sin x and cos x, 9.2 Differentiating exponentials and logarithms, 9.3 The Chain Rule, 9.4 The Product Rule, 9.5 The Quotient Rule, 9.6 Differentiating Trigonometric Functions, 9.7 Parametric Differentiation, 9.8 Implicit Differentiation, 9.9 Using Second Derivatives, and 9.10 Rates of Change, 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.
