Asolid sphere is rolling without slipping down an incline. at the bottom of the incline there is a ramp that creates a "quarter-pipe." a quarter-pipe is one quarter of a circle, when viewed from the side. the sphere is released from rest. 4 m above the bottom of the incline. the sphere rolles without slipping down the incline and back up the quarter-pipe. the sphere leaves the quarter-pipe 30 cm above the bottom of the incline and is launched vertically (straight into the air). (a) (15 points) determine the height above the bottom of the incline the ball will reach after teaving the quarter-pipe. (you may ignore any effects due to air resistance.) (b) (10 points) how would the height determined in part (a) change if the ramp were friction- less. explain, briefly. justifications should be made using concepts from class.

measure their densities same density, same sub

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.