Two shells are fired from cannon with speed `u` each, at angles of `alpha` of `beta` respectively with the horizontal.The time interval between the shots is `T`.They collide in mid air after time `t` from the first shot.Which of the following conditions must be satisfied?

Options

A. `alpha gt beta`
B. `t cos alpha=(t-T)cos beta`
C. `(t-T)cos alpha=t cos beta`
D. `(u sin alpha)t-1/2"gt"^(2)=(u sin beta)(t-T)-1/2g(t-T)^(2)`

Answer

A, B, D

Explanation

For collision
`T_(1) gt T_(2),sin alpha gt sin beta , alpha gt beta`
`x_(1)=x_(2) , t cos alpha=(t-T) cos beta`
`y_(1)=y_(2)`
`(U sin alpha)=t-1/2 "gt"^(2)=U sin beta(t-T)-1/2 g(t-T)^(2)`