A car A moves along north with velocity 30 km/h and another car B moves along east with velocity 40 km/h. The relative velocity of A with respect to B is

Options

A. 50 km/h North - East
B. 50 km/h North-West
C. 50 km/h at angle `tan^(-1)(3//4)` North of West
D. 50 km/h at angle `tan^(-1)(3//4)` West of North

Answer

C

Explanation

`therefore` Relative velocity of A w.r.t. B
`v_(AB)=v_(Ag)-v_(Bg)+(-v_(Bg))`
`|v_(AB)|=sqrt((30)^(2)+(40)^(2))=50 km//h`
`tan theta =(30)/(40)=(3)/(4)`
`theta = tan^(-1)(3//4)`


`50 km//h`, at `tan^(-1)(3//4)N` of W