What is the rate at which the wind blows? Given the following statement:
An airplane is travelling due north at an airspeed of 250 km/h when it encounters a wind from the west. The resultant ground velocity is in N20°E.
This is a trigonometry question. (recall: SOH CAH TOA)
The ratio for tangent = opposite/adjacent will help us out. Note that the resultant ground velocity is the hypotenuse.
Let w respresent the rate at which the wind blows, so
Tan (20) = w/250
Therefore, the wind is blowing from the west at 91 km/h.
Let `vecW` be the vector wind. Its magnitude is the wind speed. Its direction is west.
Let `vecA` be the airplane velocity.
`vecA+vecW` is the ground velocity written `vecG` . Its angle is 20 degree.
`vecA` , `vecW` and, `vecG` determines a right triangle because `vecA _|_ vecW `
In this triangle, the angle `(vecA, vecG)` is 20 degrees.
Therefore `tan 20=W/A`
`W=Atan 20=250tan 20=90.99` km/h
The Wind is 90.99 km/h west