Aroller coaster starts from rest at the top ofan 18m hill.
the car travels to the bottom of the hill andcontinues up the next
hill that is 10.0m high. how fast is the carmovings at the top of
the 10.0m hill if friction isignored?

12.65 m/s

Explanation:

When friction is ignored, if the car travels from 18m hill to the bottom of the hill, afterwards it travels up to a 10m hill, then overall it has traveled a distance of 18 - 10  = 8 m vertically.

If the car starts from rest, then its potential energy is converted to kinetic energy:

where m is the car mass and h is the vertical distance traveled, v is the car velocity at 10m hill

Let g = 10m/s^2. We can cancel m from both sides of the equation:

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.