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Feliz [49]
2 years 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)

Mathematics
1 answer:
katrin2010 [14]2 years ago
5 0

Answer:

Step-by-step 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=\sqrt{23.86^2+46.58^2}

\mid v_o\mid=\sqrt{2738.996}

\mid v_o\mid=52.33\ km/hr

direction \tan \theta=\frac{46.58}{23.86}

\theta =62.87^{\circ} North of east

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