Shrapnel

A bomb of mass \(M_{B}\) is located at a center of a spherical shell of mass \(M_{s}\) that has two diametrically opposed orifices subtending solid angles \(\Omega_{1}=\pi/2\) and \(\Omega_{2}=\pi/3\). The bomb explodes, isotropically, into many fragments of equal mass and velocity \(v=320~\text{m}/\text{s}\). If \(M_{s}=M_{B}\), determine the final velocity of the shell in m/s. Assume that the collisions between the fragments and the shell are perfectly inelastic and ignore gravity.

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