A profile for a streamlined racing drone winglet, symmetric about the xxx-axis, is designed using a Cartesian coordinate system. The upper boundary of the winglet is defined by the parametric equations:
x=−1.6t2 x = -1.6t^2 x=−1.6t2 y=16t−0.8t2 y = 16t - 0.8t^2 y=16t−0.8t2for 0≤t≤200 \le t \le 200≤t≤20, where x x\,x and y y\,y are measured in millimetres.
Determine the total length of the winglet along the xxx-axis.
Find an expression for dydx\displaystyle \frac{dy}{dx}dxdy in terms of ttt.
Hence, show that the maximum width of the winglet is exactly one-quarter of its total length.
35 exam-style questions on Edexcel A Level Maths 9.7 Parametric Differentiation. Each one has a worked solution and a mark scheme showing where the marks go.