(This means that the direction from which the wind blows is 45 west of the north
ID: 2889778 • Letter: #
Question
(This means that the direction from which the wind blows is 45 west of the northerly direction.) A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 200 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 ground speed 223.183 Need Help? Readit LTakto a TutoriExplanation / Answer
let velocity of wind =vw , velocity of plane with respect to air =va , velocity of plane with respect to ground =vg
wind blowing from N45oW means wind direction is towards S45oE
vw =60(cos(-45o) i +sin(-45o) j)
vw =((302) i -(302)j)
va=200(cos(90o-60o) i +sin(90o-60o) j)
va=((1003) i +(100) j)
vg=va+vw
=>vg=((1003) i +(100) j)+((302) i -(302)j)
=>vg=(1003+ 302) i +(100- 302) j
true course =N(90o-tan-1((100- 302)/(1003+ 302))) E
true course =N(90o-14.95o) E
true course =N75.1o E
ground speed =|vg|
ground speed =[(1003+ 302)2 +(100- 302)2]
ground speed =223.2 km/h
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