A 7.80-g bullet moving at 600 m/s strikes the hand of a superhero, causing the hand to move 5.90 cm in the direction of the bullet's velocity before stopping. (a) Use work and energy considerations to find the average force that stops the bullet. N (b) Assuming the force is constant, determine how much time elapses between the moment the bullet strikes the hand and the moment it stops moving. s

a)     F = 2.3797 10⁴ N, b)     t = 1.97 10⁻⁴ s

Explanation:

a) For this exercise let's use the relationship between work and scientific energy

          W = ΔK

          W = F .d

          ΔK = ½ m v² - ½ m v₀²

the bold are vectors.  in this case the force of the bullet on the hand and the displacement of the bullet has the opposite direction, therefore the angle between the two is 180. The velocity when the bullet stops is zero.

We substitute

         -F x = - ½ m vo2

         F =

let's calculate

         F =

         F = 2.3797 10⁴ N

b) let's find the acceleration

         F = ma

         a = F / m

         a = 2.3797 10⁴ / 7.80 10⁻³

         a = 3.05 10⁶ m / s²

now we can use the kinematics relations

        v = v₀ - a t

the final velocity is zero v = 0

        t = v₀ / a

        t = 600 / 3.05 10⁶

        t = 1.97 10⁻⁴ s

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.