A body A is projected upwards with velocity `v_(1)` . Another body B of same mass is projected at an angle of `45^(@)`. Both reach the same height. Calculate the ratio of their initial kinetic energies.

Explanation

As A and B attain the same height therefore vertical component of initial velocity of B is equal to initial velocity of A
`v_(2) cos 45^(@) = v_(1)` (or) `(v_(2))/(sqrt(2)) = v_(1)`
`(k_(1))/(k_(2)) = (1/2 mv_(1)^(2))/(1/2 mv_(2)^(2)) = (v_(1)^(2))/(v_(2)^(2)) = ((1)/(sqrt(2)))^(2) = 1/2`