A small airplane flies with a speed relative to the ground (ground speed) of 207

Question

A small airplane flies with a speed relative to the ground (ground speed) of 207.0 km/h in a direction 22.0 degrees to the east of north. If the plane is headed due north and the deviation from that direction is due to a cross wind blowing from west to east, what is the speed of the wind (in km/h)?

A small airplane flies with a speed relative to the ground (ground speed) of 207.0 km/h in a direction 22.0 degrees to the east of north. If the plane is headed due north and the deviation from that direction is due to a cross wind blowing from west to east, what is the speed of the wind (in km/h)?

Explanation / Answer

vp + vw = v ;

v =207 ( sin 22 i + cos 22 j ) ;

vp = vp j ;

vw = vw i ;

so

vp j + vw i = 207 ( sin 22 i + cos 22 j ) ;

or vp = 207 cos 22 = 191.927 km / hr ; <--------plane speed

and vw = 77.543 km /hr <---------wind speed

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