A plane flies at a speed of 100m/s relative to still air.There is a wind blowing

Question

A plane flies at a speed of 100m/s relative to still air.There is a wind blowing at 40m/s, 55 degrees to the east ofnorth. a) in what direction should the plane fly so as to head 10degrees west of north? b) what is the speed of the plane relative to theground? A plane flies at a speed of 100m/s relative to still air.There is a wind blowing at 40m/s, 55 degrees to the east ofnorth. a) in what direction should the plane fly so as to head 10degrees west of north? b) what is the speed of the plane relative to theground?

Explanation / Answer

let it has to fly at an angle of then the velocity of the plane in still air is given by100cosi+100sinj the velocity of the air is 40sin45j+40cos45i as 55 degrees east of north is 45 degrees north of east velocity of the plane relative to the ground is(100cos+40cos45)i+(100sin+40sin45)j if it has to fly at 10 degrees west of north we have -tan80=(100sin+40sin45)/100cos+40sin45 solve for hence the rest follows

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