1) when a spring is stretched, its length increases from 58 cm to 66 cm. calculate its extension.
2) your friend has fallen through the thin ice on a frozen pond. you come to the rescue by laying a ladder across the ice and crawling along the ladder to reach your friend. use the idea of pressure to explain why it is safer to use the ladder than to walk on the ice.

1) 8 cm    

2) Using the ladder is safer.

Explanation:

1) 66 cm - 58 cm= 8 cm

It is important to understand what is meant by 66 cm and 58 cm in the given sum. It says the length of the spring has been increased from 58 cm to 66 cm while stretching which suggest the initial length of the spring is 58 cm and final length the spring attain after stretching is 66 cm. You know that (final length) - (initial length) = extension.

2) Pressure = (Magnitude of the force)/ (area normal to the force)

A thin fragile layer of ice may not be able to bear the pressure created by your feet on it and will crack from the weakest point. Like a pin can pierce through wood by force of your thumb. But what if you decrease the pressure, like using your thumb to pierce the same piece of wood? Its not very likely to happen. The difference between the pin and the thumb is the surface area which the force is acting. So you will use a ladder which can be laid on the pond to increase the surface area which decrease the pressure created by your weight  (and your friend's when rescued) to make sure no more ice is going to be cracked!

the box does not move because you need to use a force greater than 300 n. you are only using 50 n. it needs to at least be 301 n for the box to move because then it is an unbalanced force and it will move the way that the greater force is pushing it. if you use only 300 n it will be a balanced force and will not move because the force you are exerting on the   box is the same as its force.

hope this !

im sorry if i went too in depth, i am going to include a link to a video on khan academy that will explain this.   hope that you like the video and that it explains more in detail to you.

that is the link.

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.