A plane is flying north at 200 km/h, and a wind is blowing east at 50 km/h. What is the resultant velocity of the plane?

The resultant velocity of the plane flying north at 200 km/h, with an east wind of 50 km/h, is approximately 206.15 km/h. It has an angle of about 14.04° east of north. This is calculated using the Pythagorean theorem and trigonometric functions.
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Answered by Anonymous | 2025-07-04

To find the resultant velocity of the plane, we need to consider both the velocity of the plane and the velocity of the wind as vectors. The plane is flying north with a speed of 200 km/h, and the wind is blowing east at a speed of 50 km/h.
Step-by-Step Solution:

Understand the Vectors:

The plane's velocity vector is directed north: V pl an e ​ = 200 km/h north .
The wind's velocity vector is directed east: V w in d ​ = 50 km/h east .


Create a Right Triangle:

The vectors form the two sides of a right triangle, with the plane's velocity as the vertical side (north) and the wind's velocity as the horizontal side (east).


Calculate the Resultant Velocity:

We use the Pythagorean theorem to determine the magnitude of the resultant velocity V res u lt an t ​ .

V res u lt an t ​ = 20 0 2 + 5 0 2 ​

Calculate:

V res u lt an t ​ = 40000 + 2500 ​ = 42500 ​ ≈ 206.15 km/h

Determine the Direction (Bearing):

Use trigonometry (specifically the tangent function) to find the angle θ from north towards east:

θ = tan − 1 ( 200 50 ​ )

Calculate:

θ = tan − 1 ( 0.25 ) ≈ 14.0 4 ∘


Result:
The resultant velocity of the plane is approximately 206.15 km/h at an angle of 14.0 4 ∘ east of north.
This means the plane’s effective path is slightly northeast due to the wind blowing eastward.

Answered by AvaCharlotteMiller | 2025-07-06