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

$A$ ball is projected from the ground at an angle of $45^{\circ}$ with the horizontal surface. It reaches a maximum height of $120 \ m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $30^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is.

$A$ racing car is moving with velocity $v = 40\ m/s$ on a straight track as shown. We are recording it with a camera placed at a distance of $30\ m$ from the road. Find the angular velocity (in $rad/s$) with which we should rotate the camera to record the race at the instant shown in the diagram.

$A$ strap is passing over a wheel of radius $30\, cm.$ During the time the wheel moving with an initial constant velocity of $2\, rev/s$ comes to rest,the strap covers a distance of $25\, m.$ The deceleration of the wheel in $rad/s^2$ is

$A$ $2 \ kg$ ball is thrown vertically upward and another $3 \ kg$ ball is projected with a certain angle $(\theta \neq 90^{\circ})$. Both have the same time of flight. The ratio of their maximum heights is:

$A$ particle is projected from the horizontal making an angle of $53^{\circ}$ with an initial velocity of $100\,m/s$. The time taken by the particle to make an angle of $45^{\circ}$ with the horizontal is $.........\,s$.