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JEE Main 2021 (27 Jul, Shift 2) · Relative Velocity in Two Dimensions

Relative Velocity in Two Dimensions question from JEE Main 2021 (27 Jul, Shift 2)

Q16JEE Main 2021 · 27 JUL · SHIFT 2Difficult

Relative Velocity in Two Dimensions

A swimmer wants to cross a river from point A to point B. Line AB makes an angle of 30∘^\circ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle θ\theta with the line AB should be _________∘^\circ, so that the swimmer reaches point B.

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Numerical answer type. Work it out, then open the answer.

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Answer: 30

  1. Swimmer velocity makes angle 30∘+θ30^\circ + \theta with the flow; river velocity is along the flow, both of equal magnitude.
  2. The sum of two equal vectors bisects the angle between them, so the resultant is at 30∘+θ2\frac{30^\circ + \theta}{2} from the flow.
  3. Resultant must be along AB: 30∘+θ2=30∘\frac{30^\circ + \theta}{2} = 30^\circ
  4. θ=30∘\theta = 30^\circ
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