Question

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$$\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 $(\theta_0 , \theta_1 ) = (45° , 45° ),$ the stone hits the ball after time $𝑇_1$ , and when $(\theta_0 , \theta_1 ) = (60° , 30° )$, it hits the ball after time $𝑇_2$ . In such a case,$(\frac{𝑇1 }{𝑇2} )^2$ is ______.

Answer 1

The correct answer is :2