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.
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.
