Mathematics, 12.02.2020 03:28 natalie2sheffield

Give the components of the velocity vector for wind blowing at 12 km/hr toward the southeast. (Assume north is the positive y-direction.)

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Answer from: emilyharper

$\overline{V_x} = 6\sqrt{2}\\\overline{V_y} = -6\sqrt{2}$

components can be written as:

$\overline{V} = 6\sqrt{2}\,\hat{i}-6\sqrt{2}\,\hat{j}$

Step-by-step explanation:

The components of a velocity vector at any direction can be thought of separate vectors in 'i' and 'j' directions respectively. These vectors can be added to make the resultant velocity vector.

In our case the magnitude is provided:

$|\overline{V}|= 12$

the direction is provided to be southeast:

$\theta = 45$

$\theta$ is measured from positive x-axis clockwise towards the 4th quadrant. it is important to know that quadrant since the signs of the components will be where x is positive and y is negative as the direction is south east (+x,-y).

the components of the velocity will be:

$\overline{V_x} = 12\cos{(45)} = 12\dfrac{\sqrt{2}}{2} = 6\sqrt{2}\\\overline{V_y} = -12\sin{(45)} = -12\dfrac{\sqrt{2}}{2} = -6\sqrt{2}\\$

So that:

$\overline{V} = \overline{V_x}\hat{i}+\overline{V_x}\hat{j}$

$\overline{V} = 6\sqrt{2}\,\hat{i}-6\sqrt{2}\,\hat{j}$

This can be checked using since we know that magnitude of the above vector should be 12.

$|\overline{V}| = \sqrt{(12\cos{\theta})^2+(12\sin{\theta})^2}$

$|\overline{V}| = \sqrt{(6\sqrt{2})^2+(-6\sqrt{2})^2}\\|\overline{V}| = \sqrt{36(2)+36(2)}\\|\overline{V}| = \sqrt{144} = 12\\$

Answer from: Quest

idek

step-by-step explanation:

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation:

75% of the temperatures are below what value? how do you know? 75% of the temperatures are above w

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Give the components of the velocity vector for wind blowing at 12 km/hr toward the southeast. (Assum...

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