Answer:
The answer is "512 J".
Explanation:
bullet mass [tex]m_1 = 10 g= 10^{-2} \ kg\\\\[/tex]
initial speed [tex]u_1 = 2\ \frac{Km}{s}= 2000\ \frac{m}{s}\\\\[/tex]
block mass [tex]m_2 = 4\ Kg[/tex]
initial speed [tex]v_2 =-4.2 \frac{m}{s}[/tex]
final speed [tex]v_2= 0[/tex]
Let [tex]v_1[/tex] will be the bullet speed after collision:
throughout the consevation the linear moemuntum
[tex]\to M_1V_1+m_2v_2=M_1U_1+m_2u_2\\\\\to (10^{-2} kg) V_1 +0 = (10^{-2} kg)(2000 \frac{m}{s}) + (4 \ kg)(-4.2 \frac{m}{s}) \\\\\ \to 10^{-2} v_1 = 20 -16.8\\\\[/tex]
[tex]= 320 \frac{m}{s}[/tex]
The kinetic energy of the bullet in its emerges from the block
[tex]k=\frac{1}{2} m_1 v_1^2[/tex]
[tex]=\frac{1}{2} \times 10^{-2} \times 320\\\\=512 \ J[/tex]