A cannon shell fired breaks into two equal parts at its highest point. One part retraces the path to the cannon with kinetic energy E₁ and kinetic energy of the second part is E₂ , relation between E₁ and E₂ is

Step-by-step solution

At highest point m u =- m 2 u + m 2 vm u + m 2 u = m 2 v 2 m u +m u 2 = m 2 v aligned m v & =3 m u v & =3 u aligned The kinetic energy aligned & E₁= 1 2 m 2 u^2 ^2 & E₁= 1 4 m u^2 ^2 aligned Similarly, aligned & E₂= 1 2 m 2 9 u^2 ^2 & E₂= 9 4 m u^2 ^2 aligned The relation between the E₁ and E₂ aligned & E₂=9 E₁ & E₂=9 E₁ aligned (from the Eq. (ii))