A cave explorer travels 15 m west, then 25 m north, and finally 3 m east. What is his resultant displacement ?

The resultant displacement of the cave explorer is 12 m west and 25 m north which is approximately 27.73 m in the 64.36° south of east direction from the cave explorer's initial location

Explanation:

The motion of the cave explorer are;

15 m west, 25 m north, and 3m east

The displacement, d, of the cave explorer can be displayed in vector form as follows (Taking east as positive and west as the negative direction of the ordinates);

= 3·i - 15·i + 25·j

∴ = -12·i + 25·j

The resultant displacement of the cave explorer is 12 m west and 25 m north

The magnitude and direction of the resultant displacement of the cave explorer are;

√((-12)² + 25²) ≈ 27.73 m

The direction is tan⁻¹(25/-12)  ≈ -64.36°  North of east = 64.36°  south of east

The magnitude and direction of the resultant displacement of the cave explorer are 27.73 m in a direction 64.36°  south of east.

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.