A ship moves due east at 12 m s⁻¹. A woman runs north across its deck at 5 m s⁻¹ relative to the ship. Her velocity relative to the sea is:
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A ship moves due east at 12 m s⁻¹. A woman runs north across its deck at 5 m s⁻¹ relative to the ship. Her velocity relative to the sea is:

G1 Physics · Accepted Answer

Velocity of woman relative to sea is the vector sum: v = 12î + 5ĵ. Magnitude: |v| = √(12²+5²)=13 m s⁻¹. If θ is measured north of east, tanθ = 5/12. Hence direction = tan⁻¹(5/12) north of east.