Arailway truck of mass 800 kg moving with a constant velocity of 5 m/s, collides and couples
with another railway truck of mass 6+50 kg
which is stationary. calculate the common velocity (v) with which the coupled trucks move off
after the collision.

The common velocity of truck v = 2.759 m/s

Explanation:

Given that,

Mass of first railway truck, M = 800 Kg

Mass of second railway truck, m = 650 Kg

Velocity of first railway truck, U = 5 m/s

Velocity of second truck, u = 0 m/s

According to the conservation of linear momentum,

The total momentum after impact = total momentum before impact

The mass of the truck remains the same, but the velocity after impact is coupled to be v.

Therefore,

                    Mv + mv  =  MU + mu

                          v (M+m) = MU     (u = 0)

                          v = MU/(M+m)

Substituting the values in the above equation,

                          v = 800 Kg x 5 m/s  /   (800 Kg + 650 Kg)

                          v = 2.759 m/s

Hence, the common velocity of the coupled tucks moving off after collision is v = 2.759 m/s

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.