Brittany stands at rest on a skateboard. The combined mass of Brittany and the skateboard is 62 kg. Dave tosses a 3.7-kg pumpkin to Brittany, and when she catches it, she and the skateboard begin to roll backward with a speed of 0.18 m/s.
What was the speed of the pumpkin?

3.196 m/s

Explanation:

Parameters given:

Mass of Brittany and the skateboard, M = 62 kg

Mass of pumpkin, m = 3.7 kg

Initial speed of Brittany and the skateboard, U = 0 m/s

Final velocity of Brittany, the skateboard and the pumpkin, V = v = 0.18 m/s

We can solve this problem by applying the principle of conservation of momentum.

It states that the total final momentum of a system is equal to the total initial momentum of the system.

M*U + m*u = M*V + m*v

Where u is the initial velocity of the pumpkin.

Since the final velocity of Brittany and the skateboard is equal to the final velocity of pumpkin:

M*U + m*u = (M + m) *v

Solving this to get u:

(62 * 0) + (3.7 * u) = (62 + 3.7) * 0.18

0 + 3.7u = 65.7 * 0.18

3.7u = 11.826

u = 11.826 / 3.7

u = 3.196 m/s

The initial velocity of the pumpkin was 3.196 m/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.