Answer:
R_cm = 4.66 10⁶ m
Explanation:
The important concept of mass center defined by
R_cm = 1 / M ∑ x_i m_i
where M is the total mass, x_i and m_i are the position and masses of each body
Let's apply this expression to our case.
Let's set a reference frame where the axis points from the center of the Earth to the Moon,
R_cm = 1 / M (m_earth 0 + m_moon d)
the total mass is
M = m_earth + m_moon
the distance from the Earth is zero because all mass can be considered to be at its gravimetric center
let's calculate
M = 5.98 10²⁴ + 7.35 10²²
M = 6.0535 10₂⁴24 kg
we substitute
R_cm = 1 / 6.0535 10²⁴ (0 + 7.35 10²² 3.84 )
R_cm = 4.66 10⁶ m
Answer:
1.57772 m
Explanation:
M = Mass of actor = 84.5 kg
m = Mass of costar = 55 kg
v = Velocity of costar
V = Velocity of actor
= Intial height of actor = 4.3 m
g = Acceleration due to gravity = 9.81 m/s²
As the energy of the system is conserved

As the linear momentum is conserved

Applying conservation of energy again

The maximum height they reach is 1.57772 m