Two balls with same mass and initial velocity, are projected at...

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 :

Options

A $2 \sqrt{2}: 1$
B $2: 1$
C $\sqrt{2}: 1$
D $4: 1$

Correct answer

A. $2 \sqrt{2}: 1$

Step-by-step solution

\begin{aligned} & \text{ Given, }\left(\mathrm{H}_{\max }\right)_1=8 \times\left(\mathrm{H}_{\max }\right)_2 \\ & \frac{\mathrm{u}^2 \sin ^2 \theta_1}{2 \mathrm{ g}}=8 \times \frac{\mathrm{u}^2 \sin ^2 \theta_2}{2 \mathrm{ g}} \\ & \Rightarrow \sin \theta_1=2 \sqrt{2} \sin \theta_2 \\ & \frac{\mathrm{ T}_1}{\mathrm{ T}_2}=\frac{2 \mathrm{u} \sin \theta_1 / \mathrm{g}}{2 \mathrm{u} \sin \theta_2 / \mathrm{g}}=\frac{\sin \theta_1}{\sin \theta_2}=2 \sqrt{2}\end{aligned}

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