A train moves northwards with speed `80 km h^(-1)` . While a car moves towards east with a speed of ` 60^( km h^(-1)` , what is the velocity of the train w.r.t the driver of the car ?

Explanation

let us choose the x-y co-ordinates as given below
Then the velocity of train and car are` v_(r) = 80 hatj , vecv_(C) = 60hatj`
velocity of train w.r.t the driver of the car
` vecv_(rc) = vecv_(r) - vecv_(c)`
` vecv_(rc) = 80hatj - 60hati`
` = 80 hatj + ( -60)hati`
` |vecv_(rc)|= sqrt(v_(r)^(2) + v_(c)^(2))`
` = sqrt(6400 + 3600)`
` |vecV_(rc)| = 100 ms^(-1)`
Direction of ` vecv_(rc)` in terms of angle ` theta` which it makes whit x -axis
` tan theta = (V_(rcy))/(v_(rcx))= 80/(-60)`
` theta = tan^(-1) (- 4/3)= -53.2^(@)` So to the car dirve. the train appears to move with speed ` 100 ms^(-1)` in the direction `53.2^(@)` north of west.