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1.7 Integration

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Question 42

The altitude of a specialized research probe, H(t)H(t)H(t) in kilometres, is modelled for time t>0.5 t > 0.5\,t>0.5 seconds using its vertical acceleration.

It is given that:

  • the acceleration is H′′(t)=12t2+2t2H''(t) = 12t^2 + \dfrac{2}{t^2}H′′(t)=12t2+t22​
  • the point P P\,P on the graph of altitude against time has a ttt-coordinate of 1
  • the tangent to the graph of H(t)H(t)H(t) at P P\,P has the equation H=8t−3H = 8t - 3H=8t−3
a.

Determine the equation of the normal to the graph of altitude against time at the point PPP. Give your answer in the form at+bH+c=0at + bH + c = 0at+bH+c=0, where a,b, a, b,\,a,b, and c c\,c are integers.

[3]
b.

Find an expression for H(t)H(t)H(t) in terms of ttt.

[7]

1.7 Integration Questions

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