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1 Unit 1: Pure Mathematics A

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Question 396

The altitude H H\,H of a research drone, measured in kilometres, is modelled by the curve C C\,C with equation H=f(t)H = f(t)H=f(t) for t>0t > 0t>0, where t t\,t is the time in hours since it reached a specific tracking station.

Given that

  • f′(t)=4t−(t−4)(3t+2)4tf'(t) = 4t - \dfrac{(t - 4)(3t + 2)}{4\sqrt{t}}f′(t)=4t−4t​(t−4)(3t+2)​
  • the point P(4,10)P(4, 10)P(4,10) lies on CCC
a.

find the equation of the normal to C C\,C at PPP, giving your answer in the form H=mt+cH = mt + cH=mt+c where m m\,m and c c\,c are constants to be found.

[4]
b.

find f(t)f(t)f(t), giving each term in simplest form.

[6]
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1 Unit 1: Pure Mathematics A Questions

  1. A Level
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