An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h. After flying for 0.500 h, she find sherself over a town 120 km west and 20 km south of her starting point. a) Find the wind velocity (magnitude and direction). b) If the wind velocity of 40 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 220 km/h.&nbsp;The answers are:&nbsp;a) 44.7 km/h, 26.6 deg. west of south&nbsp;b) 10.5 deg. north of west

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An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h. After flying for 0.500 h, she find sherself over a town 120 km west and 20 km south of her starting point. a) Find the wind velocity (magnitude and direction). b) If the wind velocity of 40 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 220 km/h.&amp;nbsp;The answers are:&amp;nbsp;a) 44.7 km/h, 26.6 deg. west of south&amp;nbsp;b) 10.5 deg. north of west

Anonym · Accepted Answer

If there is no wind then theplane would be at a distance  d=(220 km/h)(0.5h)=110km west of the starting point.  if the wind is blown then then the plane is 120km-110km=10km west and 20km south in the time 0.5h.  Velocity of the plane in west direction=(10km)/0.5h=20km/h  velocity of the plane in south direction=(20km)/0.5h=40km/h  Now the wind velocity is  (20kmh)2+(40kmh)2=44.7kmh  the direction is  θ=tan−1(40kmh20kmh)=63∘  south of west  b) If the wind velocity is 40km/h then the direction is  θ=sin−1(40kmh220kmh)=10.5∘  north of west

Jeffrey Jordon · Accepted Answer

The velocity of the plane relative to earth is given by  VP/E=dt=−120i^−20j^0.5=[−240i^−40j^] km/h  According to relative motion the velocity of the air relative to the earth is given by  VA/E=VP/E−VP/A  =−240i^−40j^−(−220i^)  =[−20i^−40j^] km/h  The magnitude v_{A/E} is given by  vA/E=(40)2+(20)2=44.7 km/h  the angle θ1 is given by  θ1=arctan⁡(−40−20)=63.4∘  But the angle is in 3rd quadratic so add 180  θ1=180+63.4=243.4∘  b)In this case the captain want to move with 220 km/h toward west relative to earth and wind blow in 40 km/h toward south relative to earth too , so the vectors are given by :  VP/E=[−220i^] km/h  VA/E=[−40j^] km/h  The relative velocity VP/A is given by  VP/A=VP/E−VA/E  =−220i^−(−40j^)  =[−220i^+40j^] km/h  The magnitude vP/A is given by  vP/A=(220)2+(40)2=223.6 km/h  The angle θ1 is also given by  θ2=arctan⁡(−40220)=−10.3∘  The angle θ2 is in 2nd quadratic so add 180 to get it with respect to +x -axis  θ2=180−10.3=169.7∘  Or we can say 10.3∘ north of west

An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h. After flying for 0.500 h, she find sherself over a town 120 km

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