A car is moving with a velocity of `60km//h` due east and a train is moving with a velocity of `80km//h` due south . For a passenger sitting inside the train , what is the velocity of car appearing to him ?

Explanation

Here , OA represent velocity of car `=v_(c)=60km//h`
OD represents velocity of train `=v_(T)=80 km//h`
velocity of car with respect to train is
`vec v_("CT")=vec v_(C) vec v_(T)- vec v_(C0+(-vec v_(T))`
`=vec(OA)+vec(OC)=vecOB`
`therefore |vec(OB)|=sqrt(OA^(2)+OC^(2))`
`=sqrt(60^(2)+80^(2))`
`=sqrt(10,000)=100km//h`
`tan beta =(AB)/(OA)=(80)/(60)`
`=53.06^(@)` north of east.