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
$\sqrt {{{(v\,\cos \,\theta )}^2} + {{(v\,\sin \,\theta )}^2}} $
$\sqrt {{{(v\,\cos \,\theta - v\sin \,\theta )}^2} - \,gt} $
$\sqrt {{v^2} + {g^2}{t^2} - (2\,v\,\sin \,\theta )\,gt} $
$\sqrt {{v^2} + {g^2}{t^2} - (2\,v\,\cos \,\theta )\,gt} $
A gun can fire shells with maximum speed $v_0$ and the maximum horizontal range that can be achieved is $R_{max} = \frac {v_0^2}{g}$. If a target farther away by distance $\Delta x$ (beyond $R$) has to be hit with the same gun, show that it could be achieved by raising the gun to a height at least $h = \Delta x\,\left[ {1 + \frac{{\Delta x}}{R}} \right]$.
A bullet fired at an angle of $30^o$ with the horizontal hits the ground $3.0\; km$ away. By adjusting its angle of projection, can one hope to hit a target $5.0\; km$ away ? Assume the muzzle speed to be fixed, and neglect air resistance.
A stone is projected from the ground with velocity $25\,m/s$. Two seconds later, it just clears a wall $5 \,m$ high. The angle of projection of the stone is ........ $^o$ $(g = 10m/{\sec ^2})$
Two projectiles are thrown simultaneously in the same plane from the same point. If their velocities are $v_1$ and $v_2$ at angles $\theta _1$ and $\theta_2$ respectively from the horizontal, then answer the following question
If $v_1\,\,sin\,\,\theta _1 = v_2\,\,sin\,\,\theta _2$, then choose the incorrect statement
For a given velocity, a projectile has the same range $R$ for two angles of projection if $t_1$ and $t_2$ are the times of flight in the two cases then