A projectile is thrown upward with a velocity $v_0$ at an angle $\alpha$ to the horizontal. The change in velocity of the projectile when it strikes the same horizontal plane is
$v_0 \sin \alpha$ vertically downwards
$2 v_0 \sin \alpha$ vertically downwards
$2 v_0 \sin \alpha$ vertically upwards
zero
A body of mass $0.5 \,kg$ is projected under gravity with a speed of $98 \,m/s$ at an angle of ${30^o}$ with the horizontal. The change in momentum (in magnitude) of the body is ......... $N-s$
Two projectiles are projected at $30^{\circ}$ and $60^{\circ}$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:
A ball of mass $160\, g$ is thrown up at an angle of $60^o$ to the horizontal at a speed of $10\, m\,s^{-1}$ . The angular momentum of the ball at the highest point of the trajectcry with respect to the point from which the ball is thrown is nearly ........ $kg\, m^2/s$ $(g\, = 10\, m\,s^{-2})$
The position of a projectile launched from the origin at $t = 0$ is given by $\vec r = \left( {40\hat i + 50\hat j} \right)\,m$ at $t = 2\,s$. If the projectile was launched at an angle $\theta$ from the horizontal, then $\theta$ is (take $g = 10\, ms^{-2}$)
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 $h = \Delta x\,\left[ {1 + \frac{{\Delta x}}{R}} \right]$.