Two projectiles `A` and `B` are fired simultaneously as shown in figure. They collide in air at point at time `t`.Then

Options

A. `t(u_(1)cos theta_(1)-u_(2)cos theta_(2))=20`
B. `t(u_(1)sin theta_(1)-u_(2)sin theta_(2))=10`
C. Both (a) and (b) are correct
D. Both (a) and (b) are wrong

Answer

B

Explanation

`X_(A)=X_(B)`
`:. 10+(u_(1)cos theta_(1))t=30-(u_(2)cos theta_(2))t`
or `t(u_(1)cos theta_(1)+u_(2)cos theta_(2))=20`
`y_(A)=y_(B)`
`:. 10+(u_(1)sin theta_(1))t-1/2"gt"^(2)`
`=20+(u_(2)sin theta_(2))t-1/2"gt"^(2)`
`:. (u_(1)sin theta_(1)-u_(2)sin theta_(2))t=10`