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Two ships A and B leave port P at the same time . Ship A travels due north at a steady speed of 15km/h and ship B travels N 60 degree E at a steady speed of 10km/h. what is the distance and direction from A to B after 1 hour ? what is the velocity of B relative to A ?

Solution :

I couldnt get the velocity part right .....

I resolved the two velocities along North and East , since 15 km/hr is due north it doesnt have a component along the East ...the second velocity has components along both the directions so .....

v = [ (-15 + 10 cos60)^2 + (10 sin60)^2 ]^0.5 = 13.22 km/hr

1).what i cant get is why dont i get this answer when i use the cosine rule .... is it because im using the relative velocity of A which BTW seems to be negative ???

2). I get the rigt answer if i changed the '-' part in the cosine rule to a '+'

????