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Kinematics

Problem 1.6

A ship moves along the equator to the east with velocity \(v_{0}=30 \mathrm{~km} /\) hour. The southeastern wind blows at an angle \(\varphi=60^{\circ}\) to the equator with velocity \(v=15 \mathrm{~km} / \mathrm{hour}\). Find the wind velocity \(v^{\prime}\) relative to the ship and the angle \(\varphi^{\prime}\) between the equator and the wind direction in the reference frame fixed to the ship.

Reveal Answer
v′=v02+v2+2v0vcos⁡φ≈40 km per hour, φ′=19∘v^{\prime}=\sqrt{v_{0}^{2}+v^{2}+2 v_{0} v \cos \varphi} \approx 40 \mathrm{~km} \text { per hour, } \varphi^{\prime}=19^{\circ}
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