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Velocity of swimmer w.r.t river Vₛ = 20 m/s Velocity of river w.r.t. ground Vᵣₐ₉ = 10 m/s. Vₛₐ = √Vₛᵣ² + Vᵣₐ₉² ⇒ sinθ = Vᵣₐ₉ / Vₛₐ ⇒ sinθ = 10 / 20 ⇒ sinθ = 1 / 2 ∴ θ = 30° west i.e., to cross the river along the shortest path, swimmer should make his strokes 30° west.

1. Position vector r̄ = cosωt î + sinωt ĵ.
2. Velocity vector v̄ = −ωsinωt î + ωcosωt ĵ.
3. Acceleration vector ā = −ω² cosωt î − ω² sinωt ĵ = −ω² r̄.
4. Nothing actually moves in the direction of the angular velocity vector ω̄. The direction of ω̄ simply represents that the circular motion is taking place in a plane perpendicular to it.

Correct answer: Acceleration vector ā = −ω² cosωt î − ω² sinωt ĵ = −ω² r̄.

Solution

The acceleration vector in circular motion is directed towards the center and is proportional to the negative of the position vector, as shown in option C. This matches the centripetal acceleration formula.

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