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=−1.6t2x = -1.6t^2x=−1.6t2 y=16t−0.8t2y = 16t - 0.8t^2y=16t−0.8t2
for 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.
Practise Edexcel A Level Maths 9.7 Parametric Differentiation with exam-style questions for A Level Maths. 36 questions, 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.