A motorboat is observed to travel 10 km h –1 relative to the earth in the direction 37º north of east. If the velocity of the boat due to the wind only is 2 km h –1 westward and that due to the current only is 4 km h –1 southward, what is the magnitude and direction of the velocity of the boat due to its own power ?
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km/h, 45º N of E
Sol. V = 10cos37° 
+ 10sin37° 
= 10 × 
+ 10× 
= 8 
+ 6 
8 
+ 6 
= V b + V w + V c = V b + (–2 
) + (–4 
)
V b = 10 
+ 10 
|V b | = 10 
km/h
tan θ = 
direction = 45° north of East
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