Answer to Question #113538 in Mechanics | Relativity for Stephen

Question

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"

Answer 1

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;

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

Answer: $\upsilon_{BOX}=5.39km/h.$