An airplane is flying towards its destination $300km$ due south from its present position. There is a wind blowing from the north east at $120$Km$/$hour$.$

a$.$ Draw diagram to indicate the current position of the airplane and the wind.

The plane needs to reach its destination in $30$ minutes.

b$.$ Find the direction and the speed with which the airplane must maintain in order to reach its destination on time.

c$.$ Draw a vector diagram to indicate the velocity of the wind and the airplane such that it maintains its course.