Question

Consider a ship traveling due east along the equator with velocity $v_0$. If southeastern wind blows at an angle of $' \phi '$ to the equator with velocity $'v'$, the wind velocity relative to the ship $v'$ and the angle between the equator and the wind direction in the reference frame fixed to the ship are

• A. $v' = \sqrt{v_0^2 + v^2 + v_0 v \cos \phi} , \sin^{-1} \left(\frac{v \sin \phi}{v'} \right)$
• B. $v' = \sqrt{v_0^2 + v^2 + v_0 v \sin \phi} , \cos^{-1} \left(\frac{v \cos \phi}{v'} \right)$
• C. $v' = \sqrt{v_0^2 + v^2 + v_0 v \cos \phi} , \sin^{-1} \left(\frac{v}{v'} \right)$
• D. $v' = \sqrt{v_0^2 + v^2 + v_0 v \cos \phi} , \cos^{-1} \left(\frac{v }{v'} \right)$

Answer 1

Answer: (A)

Correct answer is (a) $v' = \sqrt{v_0^2 + v^2 + v_0 v \cos \phi} , \sin^{-1} \left(\frac{v \sin \phi}{v'} \right)$