Aball of mass m is tossed vertically upward from the ground with initial velocity v. air resistance must be taken into account and its force is proportional to the square of the veloc- ity. in addition, assume the gravitational force is constant. let h(t) be the height above the ground then newton's second law leads to the initial value problem (a) find the dimensions of the constant a. (b) use dimensional analysis to find a formula for the height h of the ball in terms of t and all the parameters in the problem. identify all the dimensionless quantities. (c) introduce a useful set of dimensionless variables and parameters into the initial value problem so that there is only one parameter left multiplying the air resistance term. you need to define dimensionless time r and height y - the class notes might be useful. (d) solve the new dimensionless initial value problem exactly and compare with the prob- lem without air resistance

grav forces affect all objects magnetic forces affect magnetic objects and electric currents

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 answer is ampere

the ampere is used to measure electricity. an ampere is a unit of electric current equal. a unit of measure for the flow of current in a circuit. one ampere is the amount of current flow provided when one volt of electrical pressure is applied against one ohm of resistance.