In the locus diagrams of two projectiles 1 and 2 as shown in the fig.

Options

A. `T_(1) gt T_(2)` and `v_(0_(1)) lt v_(0_(2))`
B. `T_(1) = T_(2)` and `v_(0_(1)) lt v_(0_(2))`
C. `T_(1) = T_(2)` and `v_(0_(1)) gt v_(0_(2))`
D. `T_(1) lt T_(2)` and `v_(0_(1)) lt v_(0_(2))`

Answer

B

Explanation

Both projectile have same height.
`:. H_(1)=H_(2)`
`((u_(1)sin theta_(1))^(2))/(2g)=((u_(2)sin theta_(2))^(2))/(2g)`
`u_(1)sin theta_(1)=u_(2)sin theta_(2)`
`(2u_(1)sin theta_(1))/g=(2u_(2)sin theta_(2))/g implies T_(1)=T_(2)`
Now `(u_(1))/(u_(2))=(sin theta_(2))/(sin theta_(1)) sin theta_(1)gt theta_(2)`
`(sin theta_(1))/(sin theta_(2))gt1 implies (u_(1))/(u_(2))lt1`