The 20-g bullet is traveling at 400 m>s when it becomes embedded in the 2-kg stationary block. Determine the distance the block will slide before it stops. The coefficient of kinetic friction between the block and the plane is mk = 0.2.

distance = 4 m

Explanation:

given data

mass of bullet = 20 gm

velocity = 400 m/s

mass of stationary block = 2 kg

coefficient of kinetic friction = 0.2

solution

we will use here law of conservation of linear momentum

Momentum before collision = Momentum after collision   ...............1

here

Momentum before collision = (0.02 × 400) + 0 (stationary block)

solve we get

momentum before collision = 8 kg m/s

and

Momentum after collision = (2 + 0.02) v

put here value and we get

8 = 2.02 × v

v = 3.96 m/s.

so

as per work-energy theorem say that

KE  of the block + bullet system = work done by Friction to stop motion of the block + bullet system    ..........................2

put here value and we get

Kinetic energy = 0.5 × (2.02) × (3.96²)

Kinetic energy = 15.84 J

and

Work done by the frictional force is express as

Work done = F × (distance moved by the force)   ......................3

put here value and we get

F = μ × mg

F = 0.2 × (2.02) × (9.8)

F = 3.96 N

and

distance will be

3.96 d = 15.84

distance d =  

distance = 4 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.

the old price per ounce is c/4.

the new price per ounce is c/3.6.

the ratio of the old price to the new one is

(c/4)/(c/3.6) = (c/c)×(3.6/4) = 0.9 . . = 9/10 . . "nine tenths" in either form