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A plane has airspeed 280 km/h. The pilot wishes to fly the plane on a northern bearing. There is a 50 km/h wind blowing from S45°W. a) Draw a vector diagram to illustrate the situation. Clearly label...

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A plane has airspeed 280 km/h. The pilot wishes to fly the plane on a northern bearing. There
is a 50 km/h wind blowing from S45°W.
a) Draw a vector diagram to illustrate the situation. Clearly label the air velocity, wind velocity
and ground velocity (Va, Vw and vg can be used).
b) Calculate the heading of the plane.
c) Calculate the groundspeed.
Extracted text: A plane has airspeed 280 km/h. The pilot wishes to fly the plane on a northern bearing. There is a 50 km/h wind blowing from S45°W. a) Draw a vector diagram to illustrate the situation. Clearly label the air velocity, wind velocity and ground velocity (Va, Vw and vg can be used). b) Calculate the heading of the plane. c) Calculate the groundspeed.
Answered 85 days After Jun 02, 2022

Solution

Aditi answered on Aug 26 2022
63 Votes
SOLUTION
a.
.
c.
The blue a
ow shows the resultant vector using the cosine rule.
a2+b2﹣2bccosA
Thus, |Vg2| = 502 + 2802 - (2*50*280*cos 45°)
|Vg2| = 61101.01013
|Vg| = 247.186 km/h
This is the resultant ground speed of the plane.
From sine rule;
sin θ = sin 45 = sin θ = 0.14303 ...
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