$A$ projectile is thrown with a velocity of $10\,m/s$ at an angle of $60^{\circ}$ with the horizontal. The time interval between the moments when the speed is $\sqrt{5g}\,m/s$ is $..........\,s$ (take $g=10\,m/s^2$).

At any time $t$,the coordinates of a moving particle are $x = at^2$ and $y = bt^2$. The speed of the particle is

State whether the following statements are true or false:
$(a)$ The time of flight of a projectile depends only on the vertical component of the initial velocity.
$(b)$ The acceleration of a projectile at the maximum height is zero.
$(c)$ The maximum range of a projectile depends on the angle of projection.

Two particles,one at the centre of a circle of radius $R$,and another at a point $Q$ on the circle,start moving towards a point $P$ on the circle at the same time (see figure below). Both move with uniform velocities $\vec{V}_1$ and $\vec{V}_2$ respectively. They reach the point $P$ at the same time. If the angle between the velocities is $\theta$ and the angle subtended by $P$ and $Q$ at the centre is $\phi$ (as shown in the figure),then:

$A$ body of mass $m$ is projected at an angle of $45^{\circ}$ with the horizontal with an initial velocity $v$. If air resistance is negligible,then the total change in momentum when it strikes the ground is:

If $T$ is the total time of flight,$h$ is the maximum height,and $R$ is the horizontal range,how are the $x$ and $y$ coordinates of projectile motion related to time $t$ and range $R$?