Question

A bullet of mass m moving with velocity v strikes a block of mass M at rest and gets embeded into it. The kinetic energy of the composite block will be,

Answer 1

Dear student
$$\begin{gathered} Applyingconservationoflinearmomentumfortheblockandthebullet \\ initialmomentum \\ {P}_i=mv+0 \\ letafterthecollisionvelocityofthecombinedsystembecomes{v}_1 \\ Finalmomentum \\ {P}_f=(m+M)v_1 \\ so \\ {P}_i=P_f \\ mv=(m+M)v_1 \\ {v}_1=\frac{mv}{(m+M)}kineticenergyofthecompositesystemis \\ K=\frac{1}{2}(m+M){v^2}_1=\frac{1}{2}(m+M)(\frac{mv}{(m+M)}{)}^2 \\ K=\frac{1}{2}(m+M\left)\right(\frac{mv}{(m+M)}{)}^2=\frac{1}{2}\frac{m^2{v}^2}{(m+M)} \\ Regards \end{gathered}$$