Two spheres are projected at angles $30^{\circ}$ and $45^{\circ}$ with the horizontal. The maximum height reached by both is same. The ratio of their initial velocities is, $(\sin 45^{\circ} = \frac{1}{\sqrt{2}}, \sin 30^{\circ} = 0.5)$

Average velocity of a particle in projectile motion between its starting point and the highest point of its trajectory is: (projection speed = $u$,angle of projection from horizontal = $\theta$)

The equation for the trajectory of a projectile is $y = \left( \frac{x}{\sqrt{3}} - \frac{x^2}{60} \right) \text{ m}$. The velocity of projection of the projectile is (Acceleration due to gravity $g = 10 \text{ m s}^{-2}$) (in $\text{ m s}^{-1}$)

$A$ body of mass $M$ thrown horizontally with velocity $v$ from the top of a tower of height $H$ touches the ground at a distance of $100 \ m$ from the foot of the tower. $A$ body of mass $2M$ thrown at a velocity $\frac{v}{2}$ from the top of a tower of height $4H$ will touch the ground at a distance of ........ $m$.

$A$ gun is aimed at a target in the line of its barrel. The target is released and allowed to fall under gravity at the same instant the gun is fired. The bullet will

$A$ projectile is given an initial velocity of $(\hat{i}+2 \hat{j}) \text{ ms}^{-1}$. The equation of its path is $(g=10 \text{ ms}^{-2})$