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.

A body A is projected upwards with velocity v_(1) . Another body B of

1.	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.
Answer» Solution :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`