JEE Advanced 2024 · Paper 2, Physics question 9

A ball is thrown from the location $(x_0, y_0) = (0, 0)$ of a horizontal playground with an initial speed $v_0$ at an angle $\theta_0$ from the $+x$-direction. The ball is to be hit by a stone, which is thrown at the same time from the location $(x_1, y_1) = (L, 0)$. The stone is thrown at an angle $(180 - \theta_1)$ from the $+x$-direction with a suitable initial speed. For a fixed $v_0$, when $(\theta_0, \theta_1) = (45^{\circ}, 45^{\circ})$, the stone hits the ball after time $T_1$, and when $(\theta_0, \theta_1) = (60^{\circ}, 30^{\circ})$, it hits the ball after time $T_2$. In such a case, $(T_1/T_2)^2$ is _____.