A tran is moving with a velcoty `72 km h^(-1)` in the Noth-East direction. If abither train is moving with a vleocity `54 km h^(-1)` in the North-West direction, then what is the relative velcoity of the secons train w.r.t. the first train ?

Explanation

Refer to Fig.2 9c ) .58,
.
Velocity of first train, `vec v_(A) =vec vec (OA)`
where `vec _(A) =OA=72 km h^(-1)`
`vec (-v _(A) = vec (OC) where (OC) =(OA) =v_(A) =72 km h^(-1)`
Relative velocity of `B w. r. t. A` is
`vec _(BA) =vec v_(B) =vec _(B) + (- vev v_(A) =vec (OB) + vec (OC)`
:. `v_(BA) =sqrt((OB)^(2) +(OC)^(2) +(OB) (OC) cos 90^(0))`
`=sqrt(v_(B)^(2) +v_(A)^(2) +2 v_(B) v_(A) xx 0) ` =sqrt (54^(2) + 72^(2))`
`90 km h^(-1)`
`tan `alpha =(CD)/(OB)/(OC) =v_(B)/v_(A) =(54)/(72) =3/4 = 0.74`
`=tan 36^(0) 54'`
`alph =36 ^(0) 54'
`:. /_SOD =45^(0) +36^(0) 54'`
`=81^(00 54' West of South.