A shell of mass 200 ~g is ejected from a gun of mass 4 ~kg by an explosion that generates 1.05 ~kJ of energy. The initial velocity of the shell is

Step-by-step solution

Key Idea: In the given problem conservation of linear momentum and energy hold good. Conservation of momentum yields. aligned & m₁ v₁+m₂ y₂=0 & or 4 y₁+0.2 y₂=0 aligned Conservation of energy yields array l & 1 2 m₁ y₁^2+ 1 2 m₂ y₂^2=1050 & or 1 2 4 y₁^2+ 1 2 0.2 y₂^2=1050 & or 2 v₁^2+0.1 v₂^2=1050 array Solving Eqs. (i) and (ii), we have v₁=100 ~m / s