Enterprising students set an enormous slip-n-slide (a plastic sheet covered in water to reduce friction) on flat ground. If the slip-n-slide is 250 meters long. a. How small does the average acceleration have to be for a student starting at 5 meters/second to slide to the end?
b. If the acceleration is 0.34 m/s^2, what is the minimum initial speed a student would have to run to make it to the end? Is this speed possible?

Explanation:

a) Using the equation of motion

v² = u²+2as

v is the final velocity = 0m/s

u is the initial velocity = 5m/s

S is the distance = 250m

a is the acceleration

Substitute given values:

0² = 5²+2a(250)

-25 = 500a

a = -25/500

a = -0.05m/s²

b) If a = 0.34m/s²

We need to get the initial speed u

v² = u²+2as

0 = u²+2(0.34)(250)

-u² = 170

u² = -170

u = √-170

The square root of a negative number will give a complex number, hence the speed is not possible

protons in

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.