Answer:
[tex]E = 2910.6 J[/tex]
Explanation:
As the explosion occurs there is no external force on them
So here we can say that total momentum must be conserved
So we will have
[tex]m_1 v_1 = m_2 v_2[/tex]
in vertical direction the two parts will reach to maximum height of 12 m and 11 m respectively
So their speeds are given as
[tex]v_{y1} = \sqrt{2gh_1}[/tex]
[tex]v_{y1} = \sqrt{2(9.81)(12)} = 15.3 m/s[/tex]
[tex]v_{y2} = \sqrt{2(9.81)(11)} = 14.7 m/s[/tex]
now we have
Energy of explosion = kinetic energy of both parts after explosion
So we will have
[tex]E = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2[/tex]
[tex]E = \frac{1}{2}11(15.3)^2 + \frac{1}{2}15(14.7)^2[/tex]
[tex]E = 2910.6 J[/tex]
