A particle is projected up an inclined plane of inclination β at an elevation α, to the horizontal. Find the ratio between tan α and tan β, if the particle strikes the plane horizontally.

(a) T=2usin⁡(α−β)gcos⁡βNow we shall consider the motion of particle along OA.When the particle strikes the plane horizontallyIn this case, t=2usin⁡(α−β)gcos⁡βand 0=usin⁡α−gtusin⁡α=g2usin⁡(α−β)gcos⁡β2tan⁡β=tan⁡α⇒tan⁡α:tan⁡β=2