A plane leaves the airport on the bearing of 45 degree travelling at 400km/h. if the bearing angle are measured clockwise from the north. the wind is blowing at a bearing of 135degree at a speed of 40km/h. what is the actual velocity of the plane?

The plane's actual velocity is the vector sum of the plane's vector and the wind's vector. It will be the third side of the triangle with the given speeds as two of the sides.

The angle between the wind direction and the plane's direction is 135° -45° = 90°. That means the plane's speed will be the hypotenuse of the right triangle, and can be found using the Pythagorean theorem.

s² = 400² +40² = 161600

s = √161600 ≈ 401.995 . . . . . km/h

Plane Direction

The wind adds an angle to the plane's bearing that can be found using the sine relation:

Sin = Opposite/Adjacent

sin(θ) = 40/400 = 0.1

θ = arcsin(0.1) ≈ 5.7°

Adding this angle to the heading of the airplane gives its ground-track heading as ...

45° +5.7° = 50.7° ≈ 51°

The actual velocity of the plane is about 402 km/h on a heading of 51°.

A plane leaves the airport on the bearing of 45 degree travelling at 400km/h. if the bearing angle are measured clockwise from the north. the wind is blowing at a bearing of 135degree at a speed of 40km/h. what is the actual velocity of the plane?​

Respuesta :

Angle Difference

Plane Direction

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A plane leaves the airport on the bearing of 45 degree travelling at 400km/h. if the bearing angle are measured clockwise from the north. the wind is blowing at a bearing of 135degree at a speed of 40km/h. what is the actual velocity of the plane?