A car 'A' moves due north at a speed of `40km//hr`, while another 'B' moves due east at a speed of `30km//hr`. Find the velocity of car B relative to car A (both in magnitude and direction).

Options

A. `50 km//h NE`
B. `50 km//h NW`
C. `50 km//h`at angle `tan^(-1)(3//4) W of N`
D. `50 km//h`at angle `tan^(-1)(4//3) W of N`

Answer

C

Explanation

`vec(v)_(A//B)=vec(v)_(A//g)-vec(v)_(B//g)=vec(v)_(A//g)+(-vec(v)_(B//g))`

`|vec(v)_(A//B)|=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`