Two particles of equal mass 'm' are projected from the ground with speed `v_(1)` and `v_(2)` at angles `theta_(1)` and `theta_(2)` at the same times as shown in figure. The centre of mass of the two particles.

Options

A. will move in a vertical line if `v_(1) tan theta=v_(2) tan theta_(2)`
B. will move in a vertical line if `v_(1) sin theta=v_(2) sin theta_(2)`
C. will move In a vertical line if `v_(1) cot theta_(1)=v_(2) cot theta_(2)`
D. will move in a vertical line if `v_(1) cos theta_(1) =v_(2) cos theta_(2)`

Answer

4

Explanation

`X_(cm(t))=(v cos theta_(1)t-v_(2) cos theta_(2)t)/2`
`Y_(cm(t))=((v_(1)sin theta_(1)-g t)+(v_(2) sin theta_(2)-g t))/2`
`X_(cm)=0` when `v_(1) cos theta_(1) =v_(2) cos theta`