Show yourwork . Thank you! Suppose that a wind is blowing in the direction S45 d

Question

Show yourwork . Thank you!

Suppose that a wind is blowing in the direction S45 degree E at a speed of 50 km/h. A pilot is steering a plane in the direction N 60 degree E at an airspeed (speed in still air) of 300 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane. (Round your answers to one decimal place.) true course N [ ] degree E ground speed [ ]km/h

Explanation / Answer

velocity of plane with respect to ground = velocity of wind + velocity of plane( in still air)

taking component along East and north of both wind and plane we get

component along north = 150 - 50/sqr root 2 = 114.64

component along east = 150 *(sqr root 3) + 50/sqr root 2 = 294.86

hence tan(x) = 294.86/114.64= 2.57 hence x= arctan(2.57) = 68.73 degree

true course = N 68.73 degree E

ground speed = 304.13 km/h

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