Atugboat tows a ship with a constant force of magnitude f1. the increase in the ship's speed during a 10 s interval is 3 km/h. when a second tugboat applies an additional constant force of magnitude f2 in the same direction, the speed increases by 18 km/h during a 10 s interval. how do the magnitudes of f1 and f2 compare? (neglect the effects of water resistance and air resistance.)

 or  

In other words, is one fifth of or is five times as big as

Explanation:

In order to solve this problem we must start by sketching the situation (refer to the attached picture).

When the ship is pulled only by force 1, it will change its speed by 3km/hr in 10 seconds. So in order to use these values we need to either turn the km/hr in km/s or turn the seconds to hours. Let's turn the seconds to hours:

so we can now use the acceleration formula to find the acceleration of the boat so we get:

which will give us an accceleration of:

once we got the acceleration we can for sure say taht:

Now, if we take a look at the second drawing we can see that the resultant force applied to the boat is found by adding the two forces, force one and force two, so we get:

in this case the acceleration changes because the change in velocity is of 18km/hr in the same 10 seconds, so we get that:

so we can say that:

we can substitute the first force into this equation so we get:

and solve for the second force, so we get:

which yields:

Now we can compare theh two forces, force 1 and force 2 by dividing them:

which yields:

when solving for the first force we get:

which tells us that the second force is one fifth of the first force.

and when solving for the second force we get that:

which means that the second force is 5 times as big as the first force.

if you answer my question i will answer yours

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.