A bird is fying due east with a velocity of `4 m s^-1`. The starts to blow with a velocity of `3 ms^-1` due north. What is the magnituide of relative velocity of bird w.r.t. wind ? Find out its direction also.

Explanation

The velocity of bird with respect to wind can be given as
`vec v_(b,w) = vec v_b - vec v_w = vec v_b + (- vec v_w)`
=`4 hat i + (-3 hat j) (m s^-1)`
=`4 hat i - 3 hat j (m s^-1)`
`|vec v_(b,w)| = sqrt((4)^2 + (3)^2)`
=`5 m s^-1`
Here the direction of the relative velocity of the bird is
`|tan beta | = (3)/(4) rArr beta = tan^-1 ((3)/(4))`
Hence, the relative velocity of the bird with respect to wind is `5 m s^-1` and in the direction `tan^-1((3)/(4))` from east toward south.
.