The minute hand on a clock is 9 cm long and travels through an arc of 252 degrees every 42 minutes. to the nearest tenth of a centimeter, how far does the minute hand travel during a 42 minute period

The minutes hand travels 39.60 cm.

Explanation:

Note: a clock has a shape of a circle, the minutes hand is the radius, and the travel of the minutes hand forms a arc.

Length of an arc = ∅/360(2πr)

L = ∅/360(2πr) Equation 1π

Where L = length of an arc, ∅ = angle formed by an arc, r = radius of the arc.

Given:  ∅ = 252°, r = 9 cm, π = 3.143.

Substituting these values into equation 1,

L = 252/360(2×3.143×9)

L = 0.7×2×3.143×9

L = 39.60 cm.

Thus the minutes hand travels 39.60 cm.

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.