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 AQA A Level Maths 1.10 G: Differentiation with exam-style questions for A Level Maths. 321 questions covering 1.10.1 The derivative and second derivative, 1.10.2 Differentiating standard functions, 1.10.3 Applications of differentiation, 1.10.4 Product, quotient and chain rules (A-level only), 1.10.5 Implicit and parametric differentiation (A-level only), and 1.10.6 Constructing differential equations (A-level only), matched to the AQA A Level Maths (7357) 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.
