Two stones are projected simultaneously with same speed 10m/s from same point. The range of both are same and is equal to $5 \sqrt{3} m$ . The the difference in their time of flight is .....(g = 10 m/s²)

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$(\sqrt{3} - 1) S$

2 S

$\sqrt{3} S$

1 S

answer is C.

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Detailed Solution

If $θ_{1} = θ$ then $θ_{2} = 90 - θ$

$R = \frac{u^{2} \sin 2 θ}{g}, 5 \sqrt{3} = \frac{10 \times 10 \sin 2 θ}{10}$

$\sin 2 θ = \frac{\sqrt{3}}{2} \Rightarrow 2 θ = 60^{0}, θ = 30^{0}$

$T_{1} = \frac{2 u \sin θ_{1}}{g} = \frac{2 \times 10 \times \sin 30}{10} = 1$

$T_{2} = \frac{2 u \sin θ_{2}}{g} = \frac{2 \times 10 \times \sin 60}{10} = \sqrt{3}$

Difference in time = $(\sqrt{3} - 1)$ s

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