Two particles of equal mass in are projected from the ground with speeds `v_(1)` and `v_(2)` at angles `theta_(1)`, and `theta_(2)` as shown in the figure. Given `theta_(2)gttheta_(1)` and `v_(1)costheta_(1)=v_(2)costheta_(2)`Which statement/s is/are correct?

Options

A. Centre of mass of particles will move along a vertical line.
B. Centre of mass of particles will move along a line inclined at some angle with vertical.
C. Particle `'1'` will be above vertical. centre of mass level when both particles are in air.
D. Particle `'2'` will be above centre of mass level both particles are in air.

Answer

A, D

Explanation

`v_(cm-x)=(mv_(1)costheta_(1)m(-v_(2)costheta_(2)))/(m+m)=0`
So horizontal velocity of centre of mass is zero. Hence centre of masss will move in vertical direction.
Now `v_(2)costheta_(2)=v_(1)costheta_(1)`
`implies v_(2)/v_(1)=(costheta_(1))/(costheta_(2))gt1` (`:'theta_(2)gttheta_(1))`
`implies v_(2)gtv_(1)`
`implies v_(2)sintheta_(2)gt gt v_(1)sintheta_(1)v_(2)sintheta_(2)`
At any time particle 2 will be greater height than particle 1. so particle 2 will be above centre of man level.