Abox slides downwards at a constant velocity on an inclined surface that has a coefficient of friction uk = .58 the angle of the incline, in degrees, is most nearly:

The angle of inclination is nearly 30°

Explanation:

For a body on an inclined plane, the coefficient of friction between the body and the plane is equal to the ratio of the moving force applied to the body to the frictional force acting on the body.

If uK coefficient of friction;

Fm is the moving force

R is the normal reaction on the body

Mathematically uK = Fm/R

Fm = WSin(theta)

R = Wcos(theta)

uK = Wsin(theta)/Wcos(theta)

uK = tan(theta)

theta = arctan(uK)

If uK is 0.58

theta = arctan0.58

theta = 30°

The angle of the inclined will be 30°

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.