Example (8):
two spaceships (silver and black) are moving from the same starting point in the +
direction with constant accelerations. the silver spaceship has an initial velocity of vi
+2.00 km/s and an acceleration of +0.400 km/s2. the black spaceship has an initial >
velocity of +6.00 km/s and an acceleration of -0.400 km/s2.
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→ (a) find the time at which the silver spaceship just overtakes the black spaceship.
> (b) sketch graphs of v.(t) for the two spaceships.
(c) sketch a motion diagram showing the positions of the two spaceships at 1.0 s
interval.
(a) the position of either spaceships at later is given by:
x; =x, + 4x = x; + vix at+2, ata
when silver spaceship overtake the black, final positions are equal; thus
x; + visz at+4 at? = xin + vibx at+3at2
for both ships, the initial position was same (xis = x; thus it can be eliminated.

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.

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