You are 9.0 m from the door of your bus, behind the bus, when it pulls away with an acceleration of 1.0 m/s2. you instantly start running toward the still-open door at 5.7 m/s.

how long does it take for you to reach the open door and jump in?

what is the maximum time you can wait before starting to run and still catch the bus?

The time which the passenger can delay and still catch the bus must be less than this.

Explanation:

Given:

Now in order for the passenger to get to the door of the bus the time taken by the bus and the passenger to reach a common point must be equal.

Let them meet after x distance from the starting point of the bus.

Time taken by the passenger to reach this point:

.....................(1)

Time taken by the bus to reach this point:

Since bus starts from rest, u'=0

...................(2)

From (1) & (2)

Now we take the smallest distance: x=1.792 m

Time taken for both to reach this point: (put x in eq. (1))

Now for the maximum waiting time we find have:

Using equation of motion:

also the initial relative velocity:

and

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.

i would say