The plane must travel at 290 miles/ hour to travel 5° east of north.
What is a Vector ?
A vector is an object that has both magnitude and direction.
It is given that
The plane is travelling 0 degree North
The wind is travelling 30 degree east of north
The speed of the wind is 60 miles / hour
Resultant velocity of the plane = ? in 5 degree east direction
The resultant of the velocity vectors of plane and wind is
u ( plane ) + v( wind) = v'
In the horizontal axis
u sin 0 + v sin 30 = v'sin 5
In vertical axis
u cos 0 + v cos 30 = v' cos 5
On solving equation 1 and 2
sin 0 = 0
60 sin 30 = v' sin 5
v' = 344 miles / hour
u + 51.96 = 344 cos 5
u = 290 miles/ hour.
Therefore the plane must travel at 290 miles/ hour to travel 5° east of north.
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