Consider the following four force vectors: f1 = 50 newtons, due east f2 = 10 newtons, due east f3 = 40 newtons, due west f4 = 30 newtons, due west which two vectors add together to give a resultant with the smallest magnitude, and which two vectors add to give a resultant with the largest magnitude? in each case specify the magnitude and direction of the

F3 + F4 has the highest magnitude = 70 newtons west

and F1 + F3 has the lowest magnitude = 10 newtons east

Explanation:

F1 = 50 newtons, due east

F2 = 10 newtons, due east

F3 = 40 newtons, due west

F4 = 30 newtons, due west

Let us consider East as negative and west as positive, so

F1 = -50 newtons

F2 = -10 newtons

F3 = 40 newtons

F4 = 30 newtons

F3 + F4 = 40 + 30 = 70 newtons

F1 + F2 = -50 - 10 = -60 newtons

F1 + F3 = -50 + 40 = 10 newtons

F1 + F4 = -50 + 30 = -20 newtons

F2 + F3 = -10 + 40 = -30 newtons

F2 + F4 = -10 + 30 = 20 newtons

It can be seen that F3 + F4 has the highest magnitude = 70 newtons west

and F1 + F3 has the lowest magnitude = 10 newtons 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.