QCE Vault / Specialist Maths Vector calculus — Question 195 Original QCE Vault practice · 1 mark
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QUESTION 195 Particles move on the radius-two circle with r A = 2 ( cos t , sin t ) \mathbf r_A=2(\cos t,\sin t) r A = 2 ( cos t , sin t ) and r B = 2 ( cos ( 2 t + π ) , sin ( 2 t + π ) ) \mathbf r_B=2(\cos(2t+\pi),\sin(2t+\pi)) r B = 2 ( cos ( 2 t + π ) , sin ( 2 t + π )) . What is their first meeting time after t=0? WORKED SOLUTION
Answer B 1 mark Worked solution
Angles must differ by an integer multiple of 2 π 2\pi 2 π : 2 t + π − t = 2 k π 2t+\pi-t=2k\pi 2 t + π − t = 2 k π . Thus t = 2 k π − π t=2k\pi-\pi t = 2 k π − π , whose least positive value is pi. Both particles are then at (-2,0). Equal positions do not require identical unreduced angles. Equivalent mathematically justified methods accepted.
Exact answers unless a decimal accuracy is specified.
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