Particles P and Q move with constant velocities (î+ĵ) m s⁻¹ and (-î+2ĵ) m s⁻¹ respectively. At t=0, P is at origin and Q is at position (2î+ĵ) m. The trajectory of Q as observed by P is:
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Question

Particles P and Q move with constant velocities (î+ĵ) m s⁻¹ and (-î+2ĵ) m s⁻¹ respectively. At t=0, P is at origin and Q is at position (2î+ĵ) m. The trajectory of Q as observed by P is:

G1 Physics · Accepted Answer

Initial position of Q relative to P: rQP(0)=2î+ĵ. Relative velocity: vQP = (-î+2ĵ)-(î+ĵ) = -2î+ĵ. Hence x = 2-2t, y = 1+t. From y=1+t: t=y-1. Substitute into x: x=2-2(y-1)=4-2y. Therefore x+2y=4.