Two objects are projected at an angle $\theta^{\circ}$ and $(90-\theta)^{\circ}$ to the horizontal with the same speed. The ratio of their maximum vertical heights is

The kinetic energy of a particle moving along a circle of radius $R$ depends on the distance $s$ as $K = as^2$,where $a$ is a constant. Then the force acting on the particle is

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

$A$ person moves from $A$ to $B$ on a circular path as shown in the figure. If the distance travelled by him is $60 \, m$,then the magnitude of the displacement would be $..... \, m$. (Given $\cos 135^{\circ} = -0.7$)

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 ...... .

$A$ projectile crosses two walls of equal height $H$ symmetrically as shown in the figure. The time of flight $T$ is given by ........ $\text{s}$.