An airplane is heading north at an airspeed of 600 kmhr but

An airplane is heading north at an airspeed of 600 km/hr, but there is a wind blowing from the northeast at 40 km/hr.

The plane will end up flying degrees off course=

The plane\'s speed relative to the ground will be km/hr=

Solution

let velocity of plane with respect to wind =V_pw, velocity of wind with respect to ground =V_wg, velocity of plane with respect to ground =V_pg

V_pw=600j

wind blowing from the northeast =>wind blowing in direction of south west

V_wg=40cos225^oi +40sin225^oj

V_pg=V_pw+V_wg

V_pg=(600j)+(40cos225^oi +40sin225^oj)

V_pg=40cos225^oi +(600+40sin225^o)j

V_pg=-28.28427i +571.71573j

|V_pg|=[(-28.28427)² +(571.71573)²] =572.4

The plane\'s speed relative to the ground will be km/hr=572.4 km/hr

V_pw.V_pg=(600j).(-28.28427i +571.71573j)

V_pw.V_pg=600*571.71573

V_pw.V_pg=343029.43725

degrees off course=cos^-1([V_pw.V_pg]/[|V_pw||V_pg|])

degrees off course=cos^-1([343029.43725]_{/[600*572.41494958]})

degrees off course=2.83^o

plane will end up flying 2.83 degrees off course