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3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
Two balls are thrown simultaneously from ground with same velocity of $10\,m / s$ but different angles of projection with horizontal. Both balls fall at same distance $5 \sqrt{3}\,m$ from point of projection. What is the time interval between balls striking the ground?
  • ✓
    $(\sqrt{3}-1)\,s$
  • B
    $(\sqrt{3}+1)\,s$
  • C
    $\sqrt{3}\,s$
  • D
    $1\,s$
✓

Answer

Correct option: A.
$(\sqrt{3}-1)\,s$
a
(a)

$5 \sqrt{3}=\frac{(10)^2 \sin 2 \theta}{g} \text { or } \sin 2 \theta=\frac{\sqrt{3}}{2}$

$\therefore 2 \theta=60^{\circ} \text { or } \theta=30^{\circ}$

Two different angles of projection are therefore, $\theta$ and $\left(90^{\circ}-\theta\right)$ or $30^{\circ}$ and $60^{\circ}$.

Two different angles of projection are therefore, $\theta$ and $\left(90^{\circ}-\theta\right)$ or $30^{\circ}$ and $60^{\circ}$.

$T_1=\frac{2 u \sin 30^{\circ}}{g}=1\,s$

$T_2=2 \frac{u \sin 60^{\circ}}{g}=\sqrt{3}\,s$

$\Delta t=T_2-T_1=(\sqrt{3}-1)\,s$

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