An airplane is heading due south at a speed of 600 km h. If a wind begins blowing from the
southwest at a speed of 100 km h (average), calculate: (a) the velocity (magnitude and direction) of the
plane relative to the groun

Question

An airplane is heading due south at a speed of  600 km h. If a wind begins blowing from the 
southwest at a speed of  100 km h (average), calculate: (a) the velocity (magnitude and direction) of the 
plane relative to the groun

anonymous · Answer

Please keep in mind the wind is blowing FROM the southwesterly direction, not towards.

anonymous · Answer

You're 100% correct.  Let me fix the answer :D

anonymous · Answer

Use pythagorean theorem for speed:
$$x^2+y^2=s^2$$

 (Since the wind is moving from the southwest, you need to subtract 100/sqrt(2) km/hr to the south direction and 100/sqrt(2)km/hr to the west direction)
$$s^2=(100/(√2))^2+(600-100/(√2))^2$$

 
$$s=533.991747$$



For the direction you need to get the angle:
$$tan(α)=(−600+100/(√2)/−100/(√2))$$


$$α=262.390598$$

anonymous · Answer

Check the math, but the equations are correct :D

anonymous · Answer

Thanks a bunch. That's exactly what I got. Boy, do I hate book errors. XD

anonymous · Answer

Me too...