A ship moves along the equator to the east with velocity v 0 = 30 km/hour. The southeastern wind blows at an angle φ = 60° to the equator with velocity v = 15 km/hour. Find the wind velocity v’ relative to the ship and the angle φ ’ between the equator and the wind direction in the reference frame fixed to the ship.
Text Solution
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v’ = 
≈ 40 km per hour, φ ’ = 19°
Sol. We have
...(1)
From the vector diagram [of equation (1)] and using properties of triangle
v’ 2 = v 0 2 + v 2 – 2v 0 v cos( π – φ )
or, v’ = 
= 40 km/hr ...(2)
and 
or, sin θ = 
or θ = sin –1 
Using (2) and putting the values of v and d
θ = 19°
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