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An arrow is projected into air. Its time of flight is $5 \mathrm{~s}$ and range $200 \mathrm{~m}$. What is the maximum height reached by it? (Take $g=10 \mathrm{~m} \mathrm{~s}^{-2}$ )
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The correct answer is:
$31.25 \mathrm{~m}$
Given, $5=\frac{2 u \sin \theta}{g}$ or $\frac{u \sin \theta}{g}=\frac{5}{2}$
Maximum height $=\frac{u^2 \sin ^2 \theta}{2 g}=\frac{g}{2} \times\left(\frac{u^2 \sin ^2 \theta}{g^2}\right)$
$=\frac{g}{2} \times\left(\frac{5}{2}\right)^2=\frac{10}{2} \times \frac{25}{4}=31.25 \mathrm{~m}$
Maximum height $=\frac{u^2 \sin ^2 \theta}{2 g}=\frac{g}{2} \times\left(\frac{u^2 \sin ^2 \theta}{g^2}\right)$
$=\frac{g}{2} \times\left(\frac{5}{2}\right)^2=\frac{10}{2} \times \frac{25}{4}=31.25 \mathrm{~m}$
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