The normal force equals the magnitude of the gravitational force as a roller coaster car crosses the top of a 58-m-diameter loop-the-loop. What is the car's speed at the top?

16.87 m/s

Explanation:

To find the speed of the car at the top, when the normal force is equal the gravitational force, we just need to equate both forces:

is the centripetal acceleration in the loop:

So we have that:

So, using the gravity = 9.81 m/s^2 and the radius = 29 meters, we have:

The speed of the car is 16.87 m/s at the top.

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.