Two cars A and B move in mutually perpendicular, directions as shown in the figure . Find ` v_(BA) `
` (##AAK_T1_PHY_C02_SLV_051_Q01.png" width="80%">

Explanation

`vecv_(BA) =vecv_(B) - vecv_(B)`
`|vecv_(BA)|=|vecv_(B) -vecv_(A)|`
`sqrt(|vecv_(B)|^(2)+|vecv_(A)|^(2)-2|vecv_(B)||vecv_(A)|cos90^(@))`
` sqrt(4^(2) +3^(2)) " " (therefore |vecv_(B)|=4m//s and |vecv_(A)|=3 m//s)`
`Rightarrow |vecv_(BA)|=5m//s`
The direction of ` vecv_(BA)` is along the vector ` vecv_(B) -vecv_(A)` , which makes an angle `theta` with x-axis .
` theta = pi/2 + alpha = pi/2 + tan^(-1) (3/4) = 127^(@)`
` Rightarrow ` velocity of B relative to A is 5 m/s at an angle ` 127^(@)` with ` vecv_(A)`