A small airplane flies with a speed relative to the ground (ground speed) of 221

Question

A small airplane flies with a speed relative to the ground (ground speed) of 221.0 km/h in a direction 24 degrees to the east of north. If the plane is headed du 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 (km/h)? A small airplane flies with a speed relative to the ground (ground speed) of 221.0 km/h in a direction 24 degrees to the east of north. If the plane is headed du 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 (km/h)?

Explanation / Answer

Solution:-

vp + vw = v ;

So

v =221 ( sin 24 i + cos 24 j ) ;

vp = vp j ;

vw = vw i ;

so

vp j + vw i = 221 ( sin 24 i + cos 24 j ) ;

or vp = 221 cos 24 = 201.89 km / hr ;-plane speed

And ,vp + vw = v ;

  291.78-221=vw

=> 79.78 wind speed

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