Two cars A and B start moving from the same point with same velocity v=5km/minute. Car A moves towards North and car B in moving towards East. What is the relative velocity of B with respect to A ?

Options

A. `5sqrt2` km/min towards south-east
B. `5 sqrt2` km/min towards north-west
C. `5sqrt2` km/min towards south-west
D. `5sqrt2` km/min towards north-east

Answer

A

Explanation

The velocity of car A and car B are represented by the vectors as shown in the figure .

Given : `v_A =v_B =v=5 ` km/ minute
The relative velocity of car B w. r.t to car A is given by The direction is given by
`vec(v_(BA)) = vecv_(B) - vecv_A`
`|vecv_(BA)|=sqrt(v_B^2+(-v_A)^2+2(v_B) (-v_A) cos (90^@))`
`=sqrt((5)^(2)+(-5)^(2) +(0))=5sqrt2` km/minute
The direction `beta` is given by
`tan beta = (v_B)/(v_A) = 5/4 =1 " or " beta = 45^(@)` in south - east