Three projecties are thrown all with same speed `u` but at different angles of projection `(thetagttheta_(2)gttheta_(3))` all taken from horizontal. Maximum height attained by projectile (3) is `H`. Range of (1) `&` (3) is same `&` that of (2) is maximum for the given speed. At height `H`, speeds are `v_(1),v_(2)&v_(3)` as shown. Total time of flights are `T_(1),T_(2)&T_(3)`. Choose the correct statement(s).

Options

A. `v_(1)gtv_(2)gtv_(3)`
B. `v_(1)=v_(2)=v_(3)`
C. `T_(1)^(2),T_(2)^(2)&T_(3)^(2)` are in `AP`
D. `theta,theta_(2)&theta_(3)` are in `AP`

Explanation

from work energy theorem
`v_(1)=v_(2)=v_(3)`
`theta_(1)+theta_(2)=90^(@)&theta_(2)=45^(@)`
`rArr(theta_(1)+theta_(3))/(2)=theta_(2) rArrtheta_(1),theta_(2)&theta_(3)` are in `AP`
`T_(1)=(2usintheta_(1))/(g) rArrT_(2)=(2usin 45^(@))/(g) rArrT_(3)=(2ucostheta_(1))/(g)`
`rArr (T_(1)^(2)+T_(3)^(2))/(2)=T_(2)^(2) rArrT_(1)^(2),T_(2)^(2)&T_(3)^(2)` are in `AP`