Question

Amelia flies her airplane through calm skies at a velocity v1. The direction of v1 is 15 degrees north of east, and the speed is 180 km/hr.

Eventually, however, she enters a windy part of the atmosphere and finds that her plane now moves at a velocity v2. The direction of v2 is due east, and the speed is 150 km/hr.

What is the speed of the wind?

In what direction is the wind blowing?
(between 0 and 360 degrees)

Answer 1

The speed of the wind is 52.3 km/h

The direction of the wind is 243 degrees.

this is the right answer

Explanation:

Answer 2

Explanation:

Given

Initially Plane is flying at the speed of
`180\ km/hr`

to the
`15^(\circ)` North of east

Now wind started Blowing and plane started moving towards east with speed
`150\ km/hr`

suppose
`1v_o` is the speed of wind

So,

`\vec{v_2}=\vec{v_1}-\vec{v_o}`

`150\hat{i}=180[\cos 15\hat{i}+\sin 15\hat{j}]-\vec{v_o}`

`\vec{v_o}=\hat{i}[180\cos 15-150]+\hat{j}[180\sin 15]`

`\vec{v_o}=\hat{i}[173.866-150]+46.58\hat{j}`

`\vec{v_o}=23.86\hat{i}+46.58\hat{j}`

So magnitude of wind is

`\mid v_o\mid=√(23.86^2+46.58^2)`

`\mid v_o\mid=√(2738.996)`

`\mid v_o\mid=52.33\ km/hr`

direction
`\tan \theta=(46.58)/(23.86)`

`\theta =62.87^(\circ)` North of east