an airplane is flying to east 200k m/h which is a velocity relative to the air,while a 100km/h wind blows towards the north-east.what is its resultant velocity?we need soluion and answer for this guestion

Make your vector diagram.

You should have a triangle with sides 200 and 100 and the contained angle of 135°.
The third side is your resultant velocity, call it x

by the cosine law:
x^2 = 200^2 + 100^2 - 2(200)(100)cos 135°

continue

let me know what you get

To find the resultant velocity, we need to consider the vector sum of the airplane's velocity and the wind's velocity. Let's break down the problem into components.

The airplane's velocity is given as 200 km/h towards the east. Since this velocity is given with respect to the air, we can call it the velocity of the airplane relative to the air (Va).

The wind's velocity is given as 100 km/h towards the north-east. To find the components of this velocity, we can use trigonometry. The north-east direction can be divided into two perpendicular components: north and east.

We can represent the north component as Vw_north = Vw * cos(45°), where Vw is the wind speed (100 km/h) and 45° is the angle formed between the wind's direction and the north direction.

Similarly, the east component can be represented as Vw_east = Vw * sin(45°).

Now, let's calculate the components of the wind's velocity:

Vw_north = 100 km/h * cos(45°) = 100 km/h * 0.7071 ≈ 70.71 km/h
Vw_east = 100 km/h * sin(45°) = 100 km/h * 0.7071 ≈ 70.71 km/h

To find the resultant velocity (Vr), we can sum the components of the airplane's velocity and the wind's velocity:

Vr_north = Va + Vw_north
Vr_east = Vw_east

Vr_north = 200 km/h + 70.71 km/h = 270.71 km/h towards the north
Vr_east = 70.71 km/h towards the east

To find the magnitude and direction of the resultant velocity, we can use the Pythagorean theorem and trigonometry:

Magnitude (Vr) = sqrt(Vr_north^2 + Vr_east^2) = sqrt((270.71 km/h)^2 + (70.71 km/h)^2) ≈ 283.16 km/h

Direction angle (θ) = arctan(Vr_east / Vr_north) = arctan(70.71 km/h / 270.71 km/h) ≈ 14.18° (measured counterclockwise from the north direction towards the east direction)

Therefore, the resultant velocity of the airplane is approximately 283.16 km/h in the direction of 14.18° east of north.