To solve this problem we will use the Newtonian theory about the speed of a body in space for which the speed of a body in the orbit of a planet is summarized as:
Where,
G = Gravitational Universal Constant
M = Mass of Planet
r = Radius of the planet ('h' would be the orbit from the surface)
The escape velocity is
Through this equation we can find the mass of the Planet in function of the distance, therefore
The orbital velocity is
The time period of revolution is,
Therefore the orbital period of the satellite is closes to 1 hour and 12 min
Answer:
The horizontal distance is 4.823 m
Solution:
As per the question:
Mass of man, m = 65.0 kg
Height of the hill, H = 5.00 m
Mass of the backpack, m' = 20.0 kg
Height of ledge, h = 2 m
Now,
To calculate the horizontal distance from the edge of the ledge:
Making use of the principle of conservation of energy both at the top and bottom of the hill (frictionless), the total mechanical energy will remain conserved.
Now,
where
KE = Kinetic energy
PE = Potential energy
Initially, the man starts, form rest thus the velocity at start will be zero and hence the initial Kinetic energy will also be zero.
Also, the initial potential energy will be converted into the kinetic energy thus the final potential energy will be zero.
Therefore,
where
v = velocity at the hill's bottom
Now,
Making use of the principle of conservation of momentum in order to calculate the velocity after the inclusion, v' of the backpack:
Now, time taken for the fall:
Now, the horizontal distance is given by:
x = v't =