Two balls are thrown from an inclined plane at angle of projection `alpha` with the plane, one up the incline and other down the incline as shown in figure (`T` stands for total time of flight):

Options

A. `h_(1)=h_(2)=(v_(0)^(2)sin^(2)alpha)/(2g cos theta)`
B. `T_(1)=T_(2)=(2v_(0)sin alpha)/(g cos theta)`
C. `R_(2)-R_(1)=g(sin theta)T_(1)^(2)`
D. `v_(1)=v_(2)`

Answer

A, B, C, D

Explanation

`h_(1)h_(2)=(V_(0)^(2)sin ^(2)alpha)/(2g cos alpha)`
`T_(1)T_(2)=(2V_(0)sin alpha)/(g cos theta)`
`R_(1)=V_(0)cos alphaT_(1)-1/2g sin theta T_(1)^(2)`
`R_(2)=V_(0)cos alphaT_(1)-1/2g sin theta T_(1)^(2)`
`rArr R_(2)-R_(1)=g sin thetaT_(1)^(2)`