Two bodies are projected from the same point with equal speeds in such directions that they both strikes the same point on a plane whose inclination is β. If a be the angle of projection of the first body with the horizontal, the ratio of their times of flight is

See fig. (3) Let α be the angle of projection of the second body. The range of both the bodies will be the same. Therefore, R=u2gcos2⁡β[sin⁡(2α−β)−sin⁡β] or  sin⁡(2α−β)=sin⁡2α′−β or  2α′−β=π=(2α−β) Now,  T=2usin⁡(α−β)gcos⁡β and T′=2usin⁡α′−βgcos⁡β∴ TT′=sin⁡(α−β)sin⁡α′−β=sin⁡(α−β)sin⁡π2−(α−β)−β=sin⁡(α−β)sin⁡π2−α=sin⁡(α−β)cos⁡α