Shrapnel

A bomb of mass MBM_{B} is located at a center of a spherical shell of mass MsM_{s} that has two diametrically opposed orifices subtending solid angles Ω1=π/2\Omega_{1}=\pi/2 and Ω2=π/3\Omega_{2}=\pi/3. The bomb explodes, isotropically, into many fragments of equal mass and velocity v=320 m/sv=320~\text{m}/\text{s}. If Ms=MBM_{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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