To a person going East in a car with a velocity of `50 km h^(-1)`, a bus appears to move towards North with a velcity and direction of motion of the bus ?

Explanation

Refer to Fig. 2 . (c ) .57 , the true velocity or car, ` vec v_C = vec (OA) =50 km h^(-1) ` due East.
.
Relative velocity of bus w.r.t. car
` vec v _(BC) = vec (OB) =50 sqrt 3 km h^(-1)`, due North. ` vec v_(BC)` is
the trsultant velocity of ` vec v_(B) and - vec V_C`.
Therefore, the true velocity of bus ` (vec v_B)` must be reed by ` vec (OC). Let /_BOC= beta`. The
` v_B = OC = sqrt (BC^2 + OB^2)`
`= sqrt (50^2 + 950 sqrt 3)^2 ) = 100 km h^(-1)`
` tan beta = (BC0/(OB) = (50)/(50 sqrt 3 ) = 1/ (sqrt3) = tan 30^@`
or ` beta= 30^@ ` East of North .