Answer:
h = 206.4 m
range = 515.9 m
Explanation:
from the question we are given the following:
initial velocity (u) = 75 m/s
angle above surface = 58 degrees
acceleration due to gravity (g) = 9.8 m/s^{2}
find the maximum height (h) and the horizontal distance
maximum height (h) = 
h = 
h = 206.4 m
the horizontal distance here is the range
range = 
range = 
range = 515.9 m
<h2>The gravitational potential energy is double for stone with twice the mass of other stone.</h2>
Explanation:
Let mass of stone 1 be m.
Mass of stone 2 is twice the mass of stone 1.
Mass of stone 2 = 2m
We know that
Gravitational potential energy = Mass x acceleration due to gravity x Height
PE = mgh
For stone 1 ,
PE₁ = mgh
For stone 2 ,
PE₂ = 2mgh = 2 PE₁
So the gravitational potential energy is double for stone with twice the mass of other stone.
Answer:
Aphelion: 6404 W/m2
Perihelion: 14978 W/m2
Explanation:
The solar energy flux depends on the solar power output divided by the surface of a sphere with a radius equal to the distance to the Sun.

The distances we need are the aphelion and perihelion of Mercury.
Planetary orbits are ellipses. In an ellipse the eccentricity is related to linear eccentricity and the length of the semi major axis:

Where
e: eccentricity
c: linear eccentricity
a: semi major axis
The linear eccentricity is equal to the distance of the focus of the center of the ellipse.

a = 0.39 AU = 5.83e10 m

In planetary orbits the Sun is in one of the fucuses. With this we can calculate the prihelion and aphelion as:
Ap = a + c = 5.83e10 + 1.22e10 = 7.05e10 m
Pe = a - c = 5.83e10 - 1.22e10 = 4.61e10 m
And the solar energy fluxes will be:

