Motion

A ball is thrown from the location (x0,y0)=(0,0) of a horizontal playground with an initial speed v0 at an angle θ0 from the +x -direction. The ball is to be hit by a stone, which is thrown at the same time from the location (x1,y1)=(L,0) . The stone is thrown at an angle (180−θ1) from the +x-direction with a suitable initial speed. For a fixed v0 , when (θ0,θ1)=(45∘,45∘) , the stone hits the ball after time T1 , and when (θ0,θ1)=(60∘,30∘) , it hits the ball after time T2 . In such a case, (T1∕T2)2 is ______ .