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16 days ago

5

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)

1 answer:

lawyer [9.2K]16 days ago

5 0

Answer:

Step-by-step explanation:

Initially, the plane is traveling at a velocity of $180\ km/hr$

toward the $15^{\circ}$ north of east

Then, the wind began to blow, causing the plane to move eastward at a speed of $150\ km/hr$

Assuming $1v_o$ is the wind's speed.

Thus,

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

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

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

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

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

The magnitude of the wind is

$\mid v_o\mid=\sqrt{23.86^2+46.58^2}$

$\mid v_o\mid=\sqrt{2738.996}$

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

The direction is $\tan \theta=\frac{46.58}{23.86}$

$\theta =62.87^{\circ}$ north of east

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