Two objects are launched from the same point on a vertical line. Object 1 is projected downward with an initial speed u1. After a time delay of τ, Object 2 is projected upward from the same point with an initial speed u2. Both objects move only under the influence of gravity and air resistance is negligible.
(i) With upward taken as positive, write the general equations of motion for each object, clearly indicating the choice of time origin for each.
(ii) Derive an expression, in terms of u1,u2,τ and g, for the time measured from the instant Object 2 is launched when the two objects meet.
(iii) Show that if u1=u2, the meeting time obtained in part (ii) is independent of the common launch speed.