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.
178 exam-style questions on OCR (MEI) A Level Maths 1.5 Coordinate Geometry, covering 1.5.1 Equation of a straight line y = mx + c, 1.5.2 Gradients of parallel and perpendicular lines, 1.5.3 Distance between two points, 1.5.4 Midpoint of a line segment, 1.5.5 Form the equation of a straight line, 1.5.6 Draw a line given its equation, 1.5.7 Point of intersection of two lines, 1.5.8 Straight line models, 1.5.9 Intersection of a line and a curve, 1.5.10 Intersection of a line and a circle, 1.5.11 Equation of a circle, 1.5.12 Circle properties, 1.5.13 Parameter and parametric equations (A-level only), 1.5.14 Convert between cartesian and parametric forms (A-level only), 1.5.15 Equation of a circle in parametric form (A-level only), 1.5.16 Gradient of a parametric curve (A-level only), 1.5.17 Parametric equations in modelling (A-level only), and 1.5 Coordinate Geometry. Each one has a worked solution and a mark scheme showing where the marks go.