Figure shows top view of an airplane blown off course by wind in various directions. Assume the magnitude of the velocity of the airplane relative to the wind and the magnitude of the velocity of the wind to be the same each case. `vecv_(A//w)=`velocity of the airplane relative to the wind, `vecv_(w//g)=` velocity of the wind in ground frame

Options

A. Air plane travels fastest across the ground in case d
B. Airplane travels slowest across across the ground in case c
C. Airplane experiences in the maximum lateral displacement in case a in a given time.
D. In none of thecases, the velocity of the wind with respect to the airplanes can be directed along south west

Answer

A, B, C, D

Explanation

`vecv_(A//g)=vecv_(A//w)+vecv_(w//g)`
Net velocity of the airplane is the resultant of two given velocities.
The resultant is maximum in case d and minimum in case c.
Lateral velocity (velocity perpendicular to `vecv_(A//w)` is maximum in case a. hence lateral displacement is maximum in case a.
In each case `vecv_(A//w)` is towards north, so `vecv_(w//A)` will be towards south.