Arocket is fired vertically and ascends with a constant vertical acceleration of 20 m/s2 for 1 min. its fuel is then all used and it continues as a free fall particle. (a) calculate the maximum altitude reached. (b) calculate the total time elapsed from takeoff until the rocket strikes the earth.

a)

b)

Explanation:

Given:

Equations of motion will be used to solve get maximum altitude and total time taken

Distance travelled by the rocket during acceleration

Let v be the velocity of the rocket at the end of 60 s which is given by

a) Now the rocket will be under the gravity after its fuel ends, at the highest point of trajectory its final velocity will be zero

During this time the rocket will rise to the maximum height under gravity

Hence the maximum height of the rocket is calculated.

b) When the rocket falls back to the ground its displacement will be zero with respect to the ground

The total time

Max height= 36000 metres

Total Time of flight = 120 sec

Explanation:

It's acceleration is 20 m/s².

Time for vertical uplifting is one minute= 60 sec

V= U - at

At Max height, final velocity = zero

0 = U - at

U = at

U= 20*60

U= 1200 m/s

Formula for Max altitude

(U²Sin²tita)/2g

Max height= 1200² *( SIN90)²/(2*20)

Max height= 36000 metres

Time of flight= 2Usintita/g

= 2*1200/20

= 2400/20

= 120 sec

2 min

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.