The concept used to solve this problem is the conservation of momentum and the conservation of energy.
For conservation of the moment we have the definition:
[tex]m_1v_1 = (m_1+m_2)v_f[/tex]
Where,
m = Mass
[tex]v_1[/tex] = Initial velocity for object 1
[tex]v_f[/tex] = Final velocity
Replacing the values we have to,
[tex]m_1v_1 = (m_1+m_2)v_f[/tex]
[tex]5*12=(5+5)v_f[/tex]
[tex]v_f = 6m/s[/tex]
By conservation of energy we know that the potential energy is equal to the kinetic energy then
[tex]mgh = \frac{1}{2} m(v_f^2-v_i^2)[/tex]
[tex]gh = \frac{1}{2} v_f^2[/tex]
[tex]h = \frac{1}{2} g*v_f^2[/tex]
[tex]h = \frac{1}{2} (9.8)(6)^2[/tex]
[tex]h = 1.837m[/tex]
Therefore after the collision the height when the combined chinks will go is 1.837m
