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3-2.Motion in Plane
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A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is $v$, the total area around the fountain that gets wet is :
A$\frac{{\pi {v^2}}}{g}\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;$
B$\;\frac{{\pi {v^2}}}{{{g^2}}}$
C$\;\frac{{{\pi ^2}{v^2}}}{{{g^2}}}$
D$\;\frac{{\pi {v^4}}}{{{g^2}}}$
(AIEEE-2011)
Solution
$\begin{array}{l}
Total\,area\,around\,fountain\\
A = \pi R_{\max }^2 = \pi \frac{{{v^4}}}{{{g^2}}}\\
\left[ {\,{R_{\max }} = \frac{{{v^2}\sin 2\theta }}{g} = \frac{{{v^2}\sin {{90}^ \circ }}}{g} = \frac{{{v^2}}}{g}} \right]
\end{array}$
Total\,area\,around\,fountain\\
A = \pi R_{\max }^2 = \pi \frac{{{v^4}}}{{{g^2}}}\\
\left[ {\,{R_{\max }} = \frac{{{v^2}\sin 2\theta }}{g} = \frac{{{v^2}\sin {{90}^ \circ }}}{g} = \frac{{{v^2}}}{g}} \right]
\end{array}$
Standard 11
Physics
Similar Questions
Given that $u_x=$ horizontal component of initial velocity of a projectile, $u_y=$ vertical component of initial velocity, $R=$ horizontal range, $T=$ time of flight and $H=$ maximum height of projectile. Now match the following two columns.
| Column $I$ | Column $II$ |
| $(A)$ $u_x$ is doubled, $u_y$ is halved | $(p)$ $H$ will remain unchanged |
| $(B)$ $u_y$ is doubled $u_x$ is halved | $(q)$ $R$ will remain unchanged |
| $(C)$ $u_x$ and $u_y$ both are doubled | $(r)$ $R$ will become four times |
| $(D)$ Only $u_y$ is doubled | $(s)$ $H$ will become four times |
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