# 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...

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.

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### 2 Answers

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

0.364=w/250

w=90.99

**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**