Question

Anjali's plane had been flying through calm skies (no wind) with a velocity (speed and direction) vector
`\vec{v_1}` = (400,100). Now, however, the air mass surrounding the plane is moving quickly (i, it's windy). Although Anjali has not adjusted any of the controls in the cockpit, the plane's new velocity is
`\vec{v_2}` = (350, 50). (Speeds are in kilometers per hour.) What is the speed of the wind?

Answer 1

70.7 and3.93 radians

Step-by-step explanation:

Answer 2

The speed of the wind is 70.7 units.

Step-by-step explanation:

The velocity of the wind is equal to plane's velocity before the wind minus its velocity after the wind:

`\vec{v_(w)}=\vec{v_1}-\vec{v_2}= (400,100)- (350,50)`

`\boxed{\vec{v_(w)} = (50,50)}`

Now, the speed of the wind is the magnitude of
`\vec{v_(w)}`:

`|\vec{v_(w)}| = √(50^2+50^2)`

`\boxed{|\vec{v_(w)}| = 70.7}`

which is the speed of the wind.

P.S: No units are given for speed because no units were provided in the question.