Two balls with same mass and initial velocity, are projected at different angles in such a way that maximum height reached by first ball is 8 times higher than that of the second ball. $T_1$ and $T_2$ are the total flying times of first and second ball, respectively, then the ratio of $T_1$ and $T_2$ is

<p>Given that the maximum height reached by the first ball is 8 times that of the second ball:</p> <p>$ \left(H_{\max}\right)_1 = 8 \times \left(H_{\max}\right)_2 $</p> <p>We can relate this to the initial velocities and angles using the formula for maximum height:</p> <p>$ \frac{u^2 \sin^2 \theta_1}{2g} = 8 \times \frac{u^2 \sin^2 \theta_2}{2g} $</p> <p>Simplifying, we find:</p> <p>$ \sin \theta_1 = 2 \sqrt{2} \sin \theta_2 $</p> <p>Now, the ratio of the total flying times $T_1$ and $T_2$ is given by:</p> <p>$ \frac{T_1}{T_2} = \frac{2u \sin \theta_1 / g}{2u \sin \theta_2 / g} = \frac{\sin \theta_1}{\sin \theta_2} = 2 \sqrt{2} $</p> <p>Thus, the ratio of $T_1$ to $T_2$ is $2 \sqrt{2} : 1$.</p>