JEE MAIN - Physics (2023 - 24th January Morning Shift - No. 14)
The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :
136 m
272 m
68 m
192 m
Explanation
For vertical throw,
$$ \begin{aligned} & h=\frac{v^{2}}{2 g} \\\\ & v=\sqrt{2 g h}=\sqrt{2 g \times 136} \quad...(1) \end{aligned} $$
For max range, $\theta=45^{\circ}$
$R_{\max }=\frac{v^{2}}{g} \quad...(2)$
From (1) and (2)
$$ \begin{aligned} R_{\max } & =\frac{v^{2}}{g}=\frac{2 g \times 136}{g} \\\\ & =272 \mathrm{~m} \end{aligned} $$
$$ \begin{aligned} & h=\frac{v^{2}}{2 g} \\\\ & v=\sqrt{2 g h}=\sqrt{2 g \times 136} \quad...(1) \end{aligned} $$
For max range, $\theta=45^{\circ}$
$R_{\max }=\frac{v^{2}}{g} \quad...(2)$
From (1) and (2)
$$ \begin{aligned} R_{\max } & =\frac{v^{2}}{g}=\frac{2 g \times 136}{g} \\\\ & =272 \mathrm{~m} \end{aligned} $$
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