A plane is flying at $$ 300 \mathrm{~m} / \mathrm{s} $$ in the $$ y $$-direction. The wind is blowing at $$ 20.0 \mathrm{~m} / \mathrm{s} $$ in the $$ x $$-direction. What is the direction of the velocity of the plane? $$ \theta=[?]^{\circ} $$

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To find the direction of the velocity of the plane, we need to calculate the angle between the velocity of the plane and the positive x-axis.

Given:
- Velocity of the plane in the y-direction: $$ 300 \, \text{m/s} $$
- Wind blowing in the x-direction: $$ 20.0 \, \text{m/s} $$

Let's denote the angle between the velocity of the plane and the positive x-axis as $$ \theta $$.

We can use the tangent function to find the angle $$ \theta $$ since we have the components of the velocity in the x and y directions.

The tangent function is given by:
$$ \tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}} $$

In this case, the opposite side is the velocity of the plane in the y-direction ($$ 300 \, \text{m/s} $$) and the adjacent side is the wind blowing in the x-direction ($$ 20.0 \, \text{m/s} $$).

Therefore, we can calculate the angle $$ \theta $$ using the tangent function:
$$ \tan(\theta) = \frac{300}{20.0} $$

Now, we can solve for $$ \theta $$ by taking the inverse tangent (arctangent) of both sides:
$$ \theta = \arctan\left(\frac{300}{20.0}\right) $$

Let's calculate the value of $$ \theta $$ in degrees.
Calculate the value by following steps:
- step0: Calculate:
  $$\arctan\left(\frac{300}{20}\right)$$
- step1: Divide the terms:
  $$\arctan\left(15\right)$$
The angle $$ \theta $$ is approximately $$ 1.504228 $$ radians. To convert this to degrees, we can use the conversion factor $$ 1 \, \text{radian} = 180^\circ / \pi $$.

Therefore, the direction of the velocity of the plane is approximately $$ 1.504228 \times \frac{180^\circ}{\pi} $$ degrees.

Let's calculate the angle in degrees.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{1.504228\times 180}{\pi }$$
- step1: Multiply the numbers:
  $$\frac{270.76104}{\pi }$$
- step2: Convert the expressions:
  $$\frac{\frac{3384513}{12500}}{\pi }$$
- step3: Multiply by the reciprocal:
  $$\frac{3384513}{12500}\times \frac{1}{\pi }$$
- step4: Multiply the fractions:
  $$\frac{3384513}{12500\pi }$$
The direction of the velocity of the plane is approximately $$ 86.185916 $$ degrees.
The direction of the plane's velocity is approximately $$ 86.19^\circ $$.

A plane is flying at
in the -direction.
The wind is blowing at
in the -direction.
What is the direction of
the velocity of the plane?

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A plane is flying at in the -direction. The wind is blowing at in the -direction. What is the direction of the velocity of the plane?