A body of mass $m$ is thrown upwards at an angle $\theta$ with the horizontal with velocity $v$. While rising up the velocity of the mass after $ t$ seconds will be
A body of mass $m$ is thrown upwards at an angle $\theta$ with the horizontal with velocity $v$. While rising up the velocity of the mass after $ t$ seconds will be
- A
$\sqrt {{{(v\,\cos \,\theta )}^2} + {{(v\,\sin \,\theta )}^2}} $
- B
$\sqrt {{{(v\,\cos \,\theta - v\sin \,\theta )}^2} - \,gt} $
- C
$\sqrt {{v^2} + {g^2}{t^2} - (2\,v\,\sin \,\theta )\,gt} $
- D
$\sqrt {{v^2} + {g^2}{t^2} - (2\,v\,\cos \,\theta )\,gt} $
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- [JEE MAIN 2023]
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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
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$(D)$ Only $u_y$ is doubled
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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 |
The ratio of the speed of a projectile at the point of projection to the speed at the top of its trajectory is $x$. The angle of projection with the horizontal is
The ratio of the speed of a projectile at the point of projection to the speed at the top of its trajectory is $x$. The angle of projection with the horizontal is