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# Answer to Question #113538 in Mechanics | Relativity for Stephen

Question #113538
A "ship A" steaming in a direction 030° with a steady speed 12 km/h, sights a 'ship B'. The velocity of B relative to A is 10Km/h in a direction of 270° . Find the magnitude and direction of the velocity of "ship B"
1
2020-05-04T12:41:49-0400

Solution.

"\\upsilon_A=12km\/h;"

"\\alpha = 30^o;"

"\\upsilon_{BA}=10km\/h;"

"\\beta=270^o;"

"\\upsilon-?;"

The law of adding speeds is known:"\\overrightarrow\\upsilon_{BOX}=\\overrightarrow\\upsilon_{BA}+\\overrightarrow\\upsilon_{AOX};"

"\\overrightarrow\\upsilon_{BOX}" - body velocity B a relatively fixed frame of reference;

"\\overrightarrow\\upsilon_{BA}" -body velocity B relative to body;

"\\overrightarrow\\upsilon_{AOX}" -he velocity of the body A relative to the fixed frame of reference;

"\\upsilon_{BOX} = \\upsilon_A\\sdot cos\\alpha-\\upsilon_{BA}\\sdot cos\\beta=12km\/h\\sdot0.866-10km\/h\\sdot0.5=5.39km\/h;"

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