Erica is participating in a road race. the first part of the race is on a 5.2-mile-long straight road oriented at an angle of 25∘ north of east. the road then turns due north for another 5.0 mi to the finish line.
in miles, what is the straight-line distance from the starting point to the end of the race?

8.6 miles

Explanation:

We need to calculate the components of the total displacement along the east-west and north-south directions first.

In the first part, Erica moves 5.2 miles at 25∘ north of east. So the components of this displacement along the two directions are:

East:

North:

In the second part, Erica moves 5.0 miles north. So, the components of this displacement are:

East:

North:

So the components of the total displacement are

East:

North:

Therefore the magnitude of the displacement, which is the straight-line distance from the starting point to the end of the race, is

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scattering of light by tiny particles in air to produce the colors we see on sky, is dependent on the following factors:

(i) wavelength of light

(ii) size of the scattering particle  

(iii) distance traveled by light through the atmosphere.

according to rayleigh's law of scattering, the amount of scattering is inversely proportional to the fourth power of its wavelength. shorter the wavelength, greater is its scattering. hence violet/blue light is scattered more than red.

sun's light is a composite light ( visible light) with wavelengths in the range 400 nm (violet) to 700 nm (red). as sunlight passes through our atmosphere, the molecules of air scatter light according to their wavelengths. during sunrise and sunset, the sun's position is below the horizon. hence light from the sun travels a greater distance in the atmosphere when compared to its position a noon.

as sunlight enters the earth's atmosphere, blue light is scattered away and at the end of its journey in the sky, only red and orange wavelengths remain in the beam.

hence at sunrise and sunset, the sky appears reddish orange.