Answer to Question #227563 in Analytic Geometry for Ann

Question #227563

A jet heads due west at 350 km/h. It experience a 100km/h crosswind flowing in the direction N60 degreesW.Find the speed of the jet?


1
Expert's answer
2021-08-20T08:12:43-0400




v=(350,0),u=(100sin(60°),100cos(60°))\vec v=(-350, 0), \vec u=(-100\sin(60\degree), 100\cos(60\degree))

v+u=(350100sin(60°),0+100cos(60°))\vec v+\vec u=(-350-100\sin(60\degree), 0+100\cos(60\degree))

speed=v+uspeed=|\vec v+\vec u|

=(350100sin(60°))2+(100cos(60°))2=\sqrt{(-350-100\sin(60\degree))^2+(100\cos(60\degree))^2}

=3502+70000(32)+1002=\sqrt{350^2+70000(\dfrac{\sqrt{3}}{2})+100^2}

=10013.25+3.53 (km/h)439.456 km/h=100\sqrt{13.25+3.5\sqrt{3}}\ (km/h)\approx439.456\ km/h


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