This question can be solved from the Kepler's law of planetary motion.
As per this law the square of time period of a planet is proportional to the cube of semi major axis.
Mathematically it can be written as 
⇒
Here K is the proportionality constant.
If
and
are the orbital periods of the planets and
and
are the distance of the planets from the sun, then Kepler's law can be written as-

⇒ 
Here we are asked to calculate the the distance of Saturn from sun.It can solved by comparing it with earth.
Let the distance from sun and orbital period of Saturn is denoted as
and
respectively.
Let the distance from sun and orbital period of earth is denoted as
and
respectively.
we are given that
we know that
1 AU and
1 year.
1 AU is the mean distance of earth from the sun which is equal to 150 million kilometre.
Hence distance of Saturn from sun is calculated as -
From Kepler's law as mentioned above-

=![[1 ]^{3} *\frac{[29.46]^{2} }{[1]^{2} } AU](https://tex.z-dn.net/?f=%5B1%20%5D%5E%7B3%7D%20%2A%5Cfrac%7B%5B29.46%5D%5E%7B2%7D%20%7D%7B%5B1%5D%5E%7B2%7D%20%7D%20AU)

⇒![R_{1} =\sqrt[3]{867.8916}](https://tex.z-dn.net/?f=R_%7B1%7D%20%3D%5Csqrt%5B3%5D%7B867.8916%7D)
=9.5386 AU [ans]
Answer:

Explanation:
g = Acceleration due to gravity = 9.80 m/s²
a = Acceleration= 3.6 m/s²
= Angle = 27°
The equation is

Mass gets cancelled

Rearranging for 

The simplified expression is

*the options are incomplete. The above answer is the required solution
Answer:
Since there is no external force, there is no change (movement) in the center of mass. Internally, the center of mass might change position, but the external result is still zero net velocity.
The net recoil velocity must be zero.
Answer:
The higher the height above the more PE (Potential Energy), the body posses as seen in the formula PE = mass*gravity*height. m and g are constant hence only h affect PE
Explanation:
Potential Energy (PE) is the energy the body posses by virtue of its vertical height above the ground because, once the body is released, it will release or create some energy eg hydroelectricity power generation or a car going downhill does not need to be accelerated by the driver since it can roll over on its own due to PE
A heat pump draws heat from a cold object and rejects it to a hot one but it requires electrical energy to achieve this. Therefore, electrical energy is converted into heat energy or work in the pump's compressor. Therefore, energy is conserved.