Two buses start from a bus stand with velocitues ` 10 km h^(-1)` and ` 30 km h^(-1)` along two trachs inclined at an angle ` 60^@` . Find the distance between them agter `12 munutes.

Explanation

Displacement of 1st bus in tiem ` 12 minmute,
` vec (OP) = 10 xx (12)/( 60) = 2 km` ltbRgt Displacement of 2an bus in time ` 12 minute,
` vec (OQ) = 30 xx ( 12)/( 60) = 6 m`
Separation between the two uses after ` 12 minutes= vec (PQ)` , where
` vec (PQ) = vec (OQ)- vec (OP) = vec A- vec B= vec A+ ( -vec B)`
.
or ` PQ = sqrt (A^2 + B^@ - 2 AB cos 60^@)`
` =sqrt (6^2 + 2^2 - 2 xx 6xx 2 xx cos 60^2)`
`= 2 sqrt 7 km h^(-1)`.