A device designed to shoot projectiles consists of a spring with spring constant kmewtons/meter that has been compressed Δx meters. A marble of mass m kilograms is loaded into the device. If the entire device is at an initial height h meters and is moving at an initial velocity v meters/second, which equation best represents the magnitude of the total initial energy E, in joules, of the system? E=12mgh+12kΔx2+12mv2

E=mgh+kΔx2+mv2

E=mgh+12kΔx2+12mv2

E=mgh+kΔx2+12mv2

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.