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Rates of change and differential equations — Question 19

QCAA 2021, Paper 1 · 7 marks

Q19 · 2021 · Technology-freeComplex unfamiliar7 marks

QUESTION 19 (7 marks)

The velocity vectors of two objects A and B (in m s−1^{-1}) at time tt (in s) are given respectively by vA=6sin⁡(3t)i^+6cos⁡(3t)j^,\mathbf v_A=6\sin(3t)\hat{\mathbf i}+6\cos(3t)\hat{\mathbf j}, vB=cos⁡(t)i^−sin⁡(t)j^.\mathbf v_B=\cos(t)\hat{\mathbf i}-\sin(t)\hat{\mathbf j}. Objects A and B are initially at (−2,0,2)(-2,0,2) and (0,1,−1)(0,1,-1) respectively. Determine the position of Object A when it is 4 metres away from Object B for the first time.
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