On a different planet, a ball is fired straight upwards from the ground with an initial speed of 100 m/s. At the same instant, a second ball is dropped from the top of a cliff 400 m above the ground. The balls arrive at the same vertical location at the EXACT instant that the ball thrown upwards reaches its highest point. Determine the magnitude of the acceleration due to gravity on this planet. In other words, find g on this planet. You can assume there is no air resistance.

g = 25 m/s²

Explanation:

Since, the balls meet at the exact instant when upward thrown ball reaches its maximum point. Therefore, applying 1st equation of motion to it, we get:

Vf₁ = Vi₁ + gt

where,

g = -g (for upward motion) = acceleration due to gravity at that planet = ?

t = time

Vf₁ = Final Velocity of Upward Thrown ball = 0 m/s (ball stops at highest point)

Vi₁ = Initial Velocity of Upward Thrown Ball = 100 m/s

Therefore,

0 m/s = 100 m/s - gt

gt = 100 m/s   equation 1

Now, applying 3rd equation of motion for the height covered:

2(-g)h₁ = Vf₁² - Vi₁²

h₁ = 10000/2g

Now, we apply 2nd equation of motion to second ball moving downward:

h₂ = Vi₂t + (0.5)gt²

where,

h₂ = height covered by second ball at the time of meeting

Vi₂ = initial velocity of second ball = 0 m/s (since, it starts from rest)

Therefore,

h₂ = (0)(t) + (0.5)gt²

h₂ = (0.5)gt²

Now, it is clear from the given condition, that when the two balls meet, the sum of distance covered  by both the balls will be equal to 400 m. Therefore,

h₁ + h₂ = 400 m

using values:

10000/2g + (0.5)gt² = 400

10000 + g²t² = (400)(2g)

using equation 1:

10000 + (100)² = 800g

g = 20000/800

g = 25 m/s²

the answer would be a

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.