Two balls with same mass and initial velocity, are projected at d… - Vidyadip

MCQ

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 :

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

✓

Answer

Correct option: A.

$2 \sqrt{2}: 1$

(A) $2 \sqrt{2}: 1$
Given, $\left( H _{\max }\right)_1=8 \times\left( H _{\max }\right)_2$
$
\frac{u^2 \sin ^2 \theta_1}{2 g}=8 \times \frac{u^2 \sin ^2 \theta_2}{2 g}
$
$\begin{array}{l}\Rightarrow \sin \theta_1=2 \sqrt{2} \sin \theta_2 \\ \frac{T_1}{T_2}=\frac{2 u \sin \theta_1 / g }{2 u \sin \theta_2 / g }=\frac{\sin \theta_1}{\sin \theta_2}=2 \sqrt{2}\end{array}$

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