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Rates of change and differential equations — Question 19

QCAA 2023, Paper 1 · 6 marks

Q19 · 2023 · Technology-freeComplex unfamiliar6 marks

QUESTION 19 (6 marks)

Object A is released from the origin with constant velocity, vA\mathbf v_A, such that its position after tt seconds is given by rA(t)=23ti^+3tj^+2tk^,t≥0.\mathbf r_A(t)=2\sqrt3t\hat{\mathbf i}+3t\hat{\mathbf j}+2t\hat{\mathbf k},\quad t\ge0. At a later time, object B is released from point P(33,6,0)P(3\sqrt3,6,0) and travels towards point Q(53,8,4)Q(5\sqrt3,8,4) with constant velocity, vB\mathbf v_B, such that ∣vB∣=2∣vA∣|\mathbf v_B|=\sqrt2|\mathbf v_A|. Given that objects A and B collide, determine the time between the release of the two objects.
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