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.
82 exam-style questions on OCR A Level Maths 1.7.19 Parametric and implicit differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.