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1.5.16 Gradient of a parametric curve (A-level only)

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Question 25

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−0.8t2

for 0≤t≤200 \le t \le 200≤t≤20, where x x\,x and y y\,y are measured in millimetres.

a.

Determine the total length of the winglet along the xxx-axis.

[2]
bi.

Find an expression for dydx\displaystyle \frac{dy}{dx}dxdy​ in terms of ttt.

[2]
bii.

Hence, show that the maximum width of the winglet is exactly one-quarter of its total length.

[3]

1.5.16 Gradient of a parametric curve (A-level only) Questions

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