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

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Question 28

An aerodynamic profile for a glider wing is designed to be symmetric about the chord line (the xxx-axis). The upper boundary of the wing's cross-section is modelled by the parametric equations:

x=−1.5t2 x = -1.5t^2 x=−1.5t2 y=15t−0.75t2 y = 15t - 0.75t^2 y=15t−0.75t2

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

a.

Determine the total length of the glider wing along the xxx-axis.

[2]
bi.

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

[3]
bii.

Hence, prove that the maximum thickness (total width) of the wing is exactly one-quarter of its total length.

[4]

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

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