Kinematics

JEE Main level, single correct, medium

205 of 308

Question 205 of 308

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. T1T_1 and T2T_2 are the total flying times of first and second ball, respectively, then the ratio of T1T_1 and T2T_2 is :

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Answer: (A) 22:12 \sqrt{2}: 1

 Given, (Hmax⁡)1=8×(Hmax⁡)2u2sin⁡2θ12 g=8×u2sin⁡2θ22 g⇒sin⁡θ1=22sin⁡θ2 T1 T2=2usin⁡θ1/g2usin⁡θ2/g=sin⁡θ1sin⁡θ2=22\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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