QCEVault

Vector calculus — Question 32

Original QCE Vault practice · 7 marks

Q32 · Practice questionComplex unfamiliar7 marks

QUESTION 32 (7 marks)

Two particles move for t≥0t\ge0 with positions rA(t)=(2t,t),rB(t)=(6−t,4−2t).\mathbf r_A(t)=(2t,t),\qquad\mathbf r_B(t)=(6-t,4-2t).
a)
Show that their geometric paths cross. Determine the crossing point and the time at which each particle reaches it.
[3 marks]
b)
Determine the time at which the particles are closest to each other and their minimum separation.
[4 marks]
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