A motorboat is observed to move at 10 km h⁻¹ relative to earth in a direction 37° north of east. Wind alone produces 2 km h⁻¹ westward and current alone produces 4 km h⁻¹ southward. The boat's velocity due to its own power is:
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Question

A motorboat is observed to move at 10 km h⁻¹ relative to earth in a direction 37° north of east. Wind alone produces 2 km h⁻¹ westward and current alone produces 4 km h⁻¹ southward. The boat's velocity due to its own power is:

Options

G1 Physics · Accepted Answer

Observed ground velocity: vg = 10cos37° î + 10sin37° ĵ = 8î + 6ĵ km h⁻¹. Wind contribution = -2î. Current contribution = -4ĵ. Let vb be velocity due to engine: vg = vb - 2î - 4ĵ. Therefore vb = 10î + 10ĵ. Magnitude: |vb| = 10√2 km h⁻¹. Direction: tanθ = 10/10 =1 ⇒ θ=45° north of east.