Question

Find the total displacement in the problem below. An airplane takes off at 6:00 AM and flies a straight path at 275 km/h until 12:00 PM. Its velocity then changes to 350 km/h in the same direction until it lands at 2:30 PM. What is its average velocity the entire flight?

here are the options

775 km
1,935 km
2,385 km
2,525 km

Answer 1

Answer: 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.

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.

Explanation: