An airplane is flown in the direction 37 W of N . If the magnitude of the westerly component of the displacement is 120km . How far north does it travel?
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An airplane has a ground speed of 350 km/hr in the direction due west. If there is a wind blowing northwest at 40 km/hr, calculate the true air speed and heading of the airplane?
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Jagrata Banerjee, studied Aviation
Updated November 15, 2018 · Upvoted by Shivanshu Verma, B.Tech Electronics and Communication Engineering, Inderprastha Engineering College (2018)
Hello my friend. Thanks for the A2A…
Airspeed is the speed of the aircraft relative to the wind blowing around it.
Ground speed is the speed of the aircraft relative to the ground.
There will be higher ground speed and low true airspeed if there is a tailwind. There will be low ground speed and higher airspeed is a headwind.
Now, Ground speed = True Airspeed + Windspeed. So,
True Airspeed = Ground speed — Wind speed.
Aeronautical Calculations of Headwind and Crosswind.
Here it is given that the aircraft is moving towards west. Therefore it is heading 270 degrees at a Groundspeed of 350 kmph.
Now, the wind is blowing from Northwest.It means it is blowing from 315 degrees. The wind is blowing from NW to SE.
So, the aircraft has both headwind component as well as cross wind components.
So, angle between the wind and aircraft is therefore 315 — 270 = 45 degrees.

It is to be remembered that
Headwind = Windspeed * Cos (A).
Crosswind = Windspeed * Sin (A).
So, here, the headwind will be
HW = 40 * Cos 45 = 40 * 0.707 = 28.28 km/h.
CW = 40 * Sin 45 = 40* 0.707 =28.28 km/h.
True Airspeed (TAS) =
350 — ( — 28.28) = 350+28.28 = 378.28 km/h.
Windspeed will be negative as it is a headwind. It will be positive as it is a tailwind.
Due to the 45 degrees of cross wind, the track of the airplane will change to the below calculated Drift Angle.
Drift Angle = (Windspeed * Angle between aircraft & wind) / True Airspeed.
Drift angle = (40 *45)/378.28 = 4.75 degrees towards the Wind.
So, the drift angle will be also 4.75 degrees.

So, the new heading of the aircraft will be 274.75 degrees (West north-West); the true airspeed of the aircraft will be 378.28 km/h.
See that the groundspeed is less than the true airspeed. So, it is headwind.
Hope you got your answer. Thanks a lot..
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Prabha Mohan M Baliga, lived in Bengaluru, Karnataka, India (2019-2020)
Answered August 14, 2015
When an airplane flies in the air which itself is in motion, the velocity of the airplane undergoes a change in relation to the ground. There are two factors --- firstly, a component of the wind velocity which is perpendicular to the direction in wBhich the aircraft is pointing, will make the aircraft fly on a path which would be at an angle to the originally intended direction and, this is called 'drift'. Secondly, a component of the wind velocity that is parallel to the direction in which the aircraft is pointing, will have an effect of increase or decrease in speed of the aircraft.
To understand the concept of drift, imagine a river flowing direct from east to west. A boat on one bank of the river wants to go to a point which lies exactly north of its current location. If it sets its heading exactly towards the north on a compass and continues sailing without looking at the other shore towards the point that it intends to reach, it will finally reach a point which lies a bit towards the west due to the influence of the water flow in the river.
In this question, the aircraft is said to be moving finally in a direction due west, which means a track of 270 degrees at a speed of 350 KMPH. The wind is flowing from North-west, which means from 315 degrees at a speed of 40 KMPH. Since the angle is 45 degrees, the Sine and Cosine are equal, at approximately 70.7% and therefore, the wind component along the track and across the track are equal to 70.7% of 40 KMPH, which is equal to about 28 KMPH. Since the parallel component is against the travel direction, the ground speed is less than TAS and hence, TAS is equal to 343 KMPH. Cross wind component being equal to the same 28 KMPH, Sine of the angle (drift) is equal to 28/343. So, the drift angle is the Sine inverse of that value. The heading would be equal to the track + drift angle since the wind is from the right side. That is, approximately 5 degrees is the drift and the heading is 275 degrees.
I have approximated values in the above solution. For accuracy, use either clark's tables or a calculator.