Question

Anjali's plane had been flying through calm skies (no wind) with a velocity (speed and direction) vector -dn.net/?f=%5Cvec%7Bv_1%7D" id="TexFormula1" title="\vec{v_1}" alt="\vec{v_1}" align="absmiddle" class="latex-formula"> = (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

Answer:

The speed of the wind is 70.7 units.

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 $\vec{v_{w}}$:

$|\vec{v_{w}}| = \sqrt{50^2+50^2}$

$\boxed{|\vec{v_{w}}| = 70.7}$

which is the speed of the wind.

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