Two projectiles of same mass have their maximum kinetic energies in ratio 4: 1 and ratio of their maximum heights is also 4: 1 then what is the ratio of their ranges ?

Step-by-step solution

The kinetic energy of the projectiles is maximum at the point of release. The ratio of K.E. of projectiles aligned & 1 2 m u₁^2 1 2 m u₂^2 = 4 1 & u₁^2 u₂^2 = 4 1 aligned The ratio of maximum heights of projectiles H₁ H₂ = 4 1 aligned & u₁^2 ^2 ₁ 2 g & u₂^2 ^2 ₂ 2 g = 4 1 & u₁^2 u₂^2 ^2 ₁ ^2 ₂ = 4 1 & 4 1 ^2 ₁ ^2 ₂ = 4 1 aligned (from equation (i)) aligned & ^2 ₁= ^2 ₂ & ₁= ₂ aligned Now, ratio of ranges of projectiles aligned & R₁ R₂ = u₁^2 2 ₁ u₂^2 2 ₂ & R₁ R₂ = u₁^2 2 ₁ u₂^2 2 ₁ ( ₁= ₂ ) & R₁ R₂ = u₁^2 u₂^2 , R₁