In the figure below, a 20 kg child stands on the edge of a stationary merry-go-round of radius 3.0 m. The rotational inertia of the merry-go-round about its rotation axis is 150 kg · m2. The child catches a ball of mass 1.4 kg thrown by a friend. Just before the ball is caught, it has a horizontal velocity v (with arrow) of magnitude 14 m/s, at angle = 37° with a line tangent to the outer edge of the merry-go-round, as shown. What is the angular speed of the merry-go-round just after the ball is caught? The answer is 0.137 rad/s but I can't figure out how to solve this.

current flows in a wire

c) up is the direction the magnetic force is acting on the charge.

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.