The projectile motion of a particle of mass $5\, g$ is shown in the figure. The initial velocity of the particle is $5 \sqrt{2}\, m/s$ and the air resistance is assumed to be negligible. The magnitude of the change in momentum between the points $A$ and $B$ is $x \times 10^{-2}\, kg \cdot m/s$. The value of $x$,to the nearest integer,is ...... .

If a particle of mass $m$ covers half of the horizontal circle with constant speed $v$,then the change in its kinetic energy is

$A$ particle is moving in a circular path. The acceleration and momentum of the particle at a certain moment are $\vec{a} = (4\hat{i} + 3\hat{j}) \, m/s^2$ and $\vec{P} = (8\hat{i} - 6\hat{j}) \, kg \cdot m/s$. The motion of the particle is:

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as a function of $\phi$ can be represented as:

Two stones are projected so as to reach the same horizontal range on a horizontal surface. The maximum height reached by one exceeds the other by an amount equal to half the sum of the heights attained by them. Then,the angle of projection of the stone which attains the smaller height is $........$

Two boys conducted experiments on projectile motion with a stopwatch and noted some readings. As one boy throws a stone into the air at an angle with the horizontal,the other boy observes that after $4 \ s$,the stone is moving at an angle of $30^{\circ}$ to the horizontal,and after another $2 \ s$,it is traveling horizontally. The magnitude of the initial velocity of the stone is (Acceleration due to gravity,$g = 10 \ ms^{-2}$):