a 8 8 APPARENT HEIGHT (KM) 200 40 1. i sO 60 70 ELAPSED TIME AFTER DETONATION (MIM) ° / 60 90 Fige 3.19 = Apparent Minimum Height of Groupi: of Echoes at Rongerik from 40 to 95 min after Shot 4, with Fitted Hyperbolic Curves Assuming that the point of reflection moved horizontally at a height h with a velocity v, passing overhead at time to, the slant vange R at time t may be found from the right~triangular relationship By selecting three well-distributed points which represent the-trend of the sequence between plus 40 and 70 min, it is possible to establish values of h, v, and to which yield the first hyperbolic curve shown in Fig. 3.19. Equatio 3.1 may be solved for h, v, and to in terms of the three selected points (R1, t13 Ra, t23; R3, +3) to give to = 1/2 B12 (ta2=tf) + R22 (te2— 12) + Ry? (ty2—t22) ‘ Ry2 (ty = t3) + RoA(ty ~ ty) + Rer(t, ty) v= he [ Ro*_ = Ry? (tz - ty) (tg + ty - 2ty) [m2-2% Ye (ty - t,)*| 1/2 pe SECRET > (3.2)