A political party has to start its procession in an area where wind is blowing at a speed of `30 sqrt(2) km h^-1` and party flags on the cars are fluttering along north - east direction. If the procession starts with a speed of `40 km h^-1` towards north, find the direction of flags on the cars.

Explanation

When the procession is stationary, the flags flutter along the north - east direction. It means wind is flowing along the north - east direction. The flags will start fluttering along the direction of the relative velocity of wind w.r.t. procession.
`vec v_(w c) = vec v_w - vec v_c`
=`(30 sqrt(2) cos 45^@ hat i + 30 sqrt(2) sin 45^@ hat j) - 40 hat j`
=`30 hat i - 10 hat j (m s^-1)`
`tan theta = (10)/(30) = (1)/(3)`
So the flag will flutter in a direction at `theta = tan^-1 (1//3)` S of E.
.