QCEVault

Vectors in three dimensions — Question 108

Original QCE Vault practice · 7 marks

Q108 · Practice questionComplex unfamiliar7 marks

QUESTION 108 (7 marks)

A drone and a moving beacon have positions rD(t)=(2t,t),rB(t)=(8cos⁡(0.4t),8sin⁡(0.4t)),0≤t≤6.\begin{aligned}\mathbf r_D(t)&=(2t,t),\\\mathbf r_B(t)&=(8\cos(0.4t),8\sin(0.4t)),\end{aligned}\qquad0\le t\le6. Coordinates are in kilometres and tt is in hours.
Supporting diagram for question 108
a)
Construct an expression for the square of the separation between the drone and beacon.
[2 marks]
b)
Use technology to determine the time of closest approach and the minimum separation, to three decimal places.
[3 marks]
c)
Determine the magnitude of the relative velocity at the time of closest approach, to three decimal places.
[2 marks]
Question linkSyllabus coverage

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