On an inclined plane, two particles A and B are projected with the same speed at the same angle with the horizontal, particle A down and particle B up the plane. If the ratio of time of flight of A and B is cot θ , where θ is the angle at which B is projected as measured from inclined plane, find the angle with horizontal at which particles are projected.

Step-by-step solution

Let, α be the angle of projection of B and β be the angle of elevation of the inclined plane as shown in the diagram below and t x denote the time period of particle x . Then, t A = 2 u   sin α + β g   cos β and t B = 2 u   sin ( α - β )   g   cos β t A t B = sin ( α + β ) sin ( α - β ) As given in the question, θ is the angle at which the particle B is projected as measured from the inclined plane, that is, α - β &#