Two particles are projected from a point at the same instant with velocities whose horizontal and vertical components are `u_(1), v_(1)` and `u_(2), v_(2)` respectively. Prove that the interval between their passing through the other common point of their path is
`(2(v_(1)u_(2) - v_(2) u_(1)))/(g (u_(1) + u_(2))`

Options

A. `(2)/(g)((v_(1)u_(1)-v_(2)v_(2))/(u_(1)+u_(2)))`
B. `(2)/(g)((v_(1)^(2)+v_(2)^(2))/(u_(1)+u_(2)))`
C. `(2)/(g)((u_(1)^(2)+u_(2)^(2))/(v_(1)+v_(2)))`
D. `(2)/(g)((v_(1)u_(2)-v_(2)u_(1))/(u_(1)+u_(2)))`

Answer

A