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A stone projected from the ground with a velocity $50 \mathrm{~ms}^{-1}$ at an angle of $30^{\circ}$ with the horizontal crosses a wall after a time of $3 \mathrm{~s}$. Then the horizontal distance beyond the wall that the stone strikes the ground is $\left(\right.$ acceleration due to gravity $\left.=10 \mathrm{~ms}^{-2}\right)$
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Verified Answer
The correct answer is:
$86.6 \mathrm{~m}$
Velocity of stone, $u=50 \mathrm{~m} / \mathrm{s}$
Range, $\mathrm{R}=\frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{g}}$
$$
\begin{aligned}
& =\frac{50^2 \sin 60}{10} \\
& =\frac{2500 \times \sqrt{3}}{2 \times 10} \\
& =216.5 \mathrm{~m}
\end{aligned}
$$
Time of flight, $\mathrm{T}=\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}}$
$$
\begin{aligned}
& =\frac{2 \times 50 \times \sin 30}{10}=10 \times \frac{1}{2}=5 \mathrm{~s} \\
& \frac{\mathrm{t}}{\mathrm{T}}=\frac{\mathrm{x}}{\mathrm{R}} \\
& \Rightarrow \mathrm{x}=\frac{\mathrm{Rt}}{\mathrm{T}}=\frac{216.5 \times 3}{5}=129.9 \mathrm{~m}
\end{aligned}
$$
The distance beyond the wall where the stone will hit,
$$
\therefore R-x=216.5-129.9=86.6 m
$$
Range, $\mathrm{R}=\frac{\mathrm{u}^2 \sin 2 \theta}{\mathrm{g}}$
$$
\begin{aligned}
& =\frac{50^2 \sin 60}{10} \\
& =\frac{2500 \times \sqrt{3}}{2 \times 10} \\
& =216.5 \mathrm{~m}
\end{aligned}
$$
Time of flight, $\mathrm{T}=\frac{2 \mathrm{u} \sin \theta}{\mathrm{g}}$
$$
\begin{aligned}
& =\frac{2 \times 50 \times \sin 30}{10}=10 \times \frac{1}{2}=5 \mathrm{~s} \\
& \frac{\mathrm{t}}{\mathrm{T}}=\frac{\mathrm{x}}{\mathrm{R}} \\
& \Rightarrow \mathrm{x}=\frac{\mathrm{Rt}}{\mathrm{T}}=\frac{216.5 \times 3}{5}=129.9 \mathrm{~m}
\end{aligned}
$$
The distance beyond the wall where the stone will hit,
$$
\therefore R-x=216.5-129.9=86.6 m
$$
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