According to Ideal gasTo solve this problem, the fastest relationship allows us to observe the proportionality between the two variables would be the one expressed in the ideal gas equation, which is

Here
P = Pressure
V = Volume
N = Number of moles
R = Gas constant
T = Temperature
We can see that the pressure is proportional to the temperature, then

This relationship can be extrapolated to all the scenarios in which these two variables are related. As the pressure increases the temperature increases. The same goes for the pressure in the atmosphere, for which an increase in this will generate an increase in temperature. This variable can be observed in areas of different altitude. At higher altitude lower atmospheric pressure and lower temperature.
To develop this problem it is necessary to apply the concepts related to Gravitational Potential Energy.
Gravitational potential energy can be defined as

As M=m, then

Where,
m = Mass
G =Gravitational Universal Constant
R = Distance /Radius
PART A) As half its initial value is u'=2u, then



Therefore replacing we have that,

Re-arrange to find v,



Therefore the velocity when the separation has decreased to one-half its initial value is 816m/s
PART B) With a final separation distance of 2r, we have that

Therefore




Therefore the velocity when they are about to collide is 
Answer:
1. Electromagnetic waves travel in a vacuum whereas mechanical waves do not.
2. The ripples made in a pool of water after a stone is thrown in the middle are an example of mechanical wave. Examples of electromagnetic waves include light and radio signals.
3. Mechanical waves are caused by wave amplitude and not by frequency. Electromagnetic Waves are produced by vibration of the charged particles.
4. While an electromagnetic wave is called just a disturbance, a mechanical wave is considered a periodic disturbance.
Explanation:
Increasing its velocity will add to the kinetic energy more as the formula for kinetic energy is 0.5*m*v^2. (The speed will be squared making it greater)
Answer:
The new intensity decreases by a factor of 16.
Explanation:
The intensity of sound wave is given by :

P is power
A is area

or
, r is distance from the source
If the distance from the source is increased by a factor of 4, r' = 4r
So,

So, the new intensity decreases by a factor of 16.