The apollo lunar module was used to make the transition from the spacecraft to the moon's surface and back. consider a similar module for landing on the surface of mars. use conservation of mechanical energy to answer these questions.

(a) as the lander is descending, if the pilot decides to shut down the engine when the lander is at a height of 2.7 m, (this may not be a safe height to shut down the engine) and the velocity of the lander (relative to the surface of the planet) is 1.8 m/s what will be velocity of the lander at impact? note: g on the surface of mars is about 0.4 times that on the surface of the earth.

(b) in the case of the lunar module an impact velocity of 3.0 m/s or less was essential for a safe landing. assuming this to be the case for the mars lander as well, at what maximum height could the pilot shut down the engines to ensure a safe landing. assume the velocity v0 at the time the engine is shut down is 1.8 m/s.

a) 4.94263 m/s

b) 0.734 m

Explanation:

t = Time taken

u = Initial velocity

v = Final velocity

s = Displacement

g = Acceleration due to gravity

The impact velocity of the rocket will be 4.94263 m/s

The maximum height the pilot could shut down the engines to ensure a safe landing at initial velocity 1.8 m/s and final velocity 3 m/s is 0.734 m

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.