Suppose two particles `1 and 2` are projected in vertical plane simultaneously.
Their angles of projection are `30^@ and theta`, respectively, with the horizontal. Let they collide after a time`t` in air. Then
.

Options

A. `theta=sin^(-1)(4/5)` and they will have same speed just before the collision
B. `theta=sin^(-1)(4/5)` and they will have different speed just before the collision
C. `xlt1280sqrt(3)-960m`
D. It is possible that the particles collide when both of them are at their highest point

Answer

B, C, D

Explanation

If they collide, their vertical components of velocities should be same i.e.
`100sintheta=160sin30^(@)impliessintheta=4//5`
Their vertical components will always be same. Horizontal components
`16cos30=80sqrt(3)ms^(-1)`
and `100 cos theta=100xx3//5=60ms^(-1)`
They are to same hence their velocities will not be same at any time so b is correct
`x=x_(1)-x_(2)`
`=10cos30^(@)t-100costhetat`

`implies x=(80sqrt(3)-60)t`
Time of flight `T=(2xx160xxsin30^(@))/g=16s`
Now `tltTrarr ` to collide in air
`implies x/(80sqrt(3)-60)lt16impliesxlt1280sqrt(3)-960`
Since their times of flight are same, they will simultaneously reach their maximum height. so it is possible to collide at highest point for certain values of `x`.