A small ball is to be thrown, so as to just pass through three equal rings of diameter 2m and placed in parallel vertical planes at distance 8 m apart with their highest points at height 32 m above the point of projection as shown in the figure. If the angle of projection with horizontal is α. The value of tan α is ______.

In figure, points A,B and C are lying on the trajectory of the path of the ball. The equation of trajectory isy=xtan⁡α−gx22u2cos2⁡αFor point A,    32−2=xtan⁡α−5x2u2cos2⁡α Or     30=xtan⁡α−5u2x21+tan2⁡α    ......(i)For point B,32=(x+8)tan⁡α−5u2(x+8)21+tan2⁡α   .......(ii)For point C, 32−2=(x+8)tan⁡α−5(x+16)2u21+tan2⁡α⇒ 30=(x+16)tan⁡α−5(x+16)21+tan2⁡αu2    .....(iii)Subtracting Eq. (i) from Eq. (ii), 2=8tan⁡α−5u2(1+tan⁡α)x2+16x+64−x2⇒ 2=8tan⁡α−5u21+tan2⁡α(16x+64)      .......(iv)Subtracting Eq. (i) from Eq (iii),0=16tan⁡α−51+tan2⁡αu2x2+32x+256−x2   ....(v)From Eq. (iv) and Eq.   tan2⁡α=32×264=1∴ tan⁡α=1