$A$ body is projected at an angle $\theta$ so that its range is maximum. If $T$ is the time of flight, then the value of maximum range is (acceleration due to gravity $= g$)

At the highest point of the path of a projectile,its

$A$ particle $P$ is projected with velocity $u_1$ at an angle of $30^\circ$ with the horizontal. Another particle $Q$ is projected vertically upwards with velocity $u_2$ from the point directly below the maximum height of $P$. The condition for the collision of both particles is:

Two projectiles are fired from the same point with the same speed at angles of projection $60^\circ$ and $30^\circ$ respectively. Which one of the following is true?

$A$ boy throws a ball into the air at $45^{\circ}$ from the horizontal to land it on the roof of a building of height $H$. If the ball attains maximum height in $2 \text{ s}$ and lands on the building in $3 \text{ s}$ after launch, then the value of $H$ is . . . . . . $\text{m}$. $(g = 10 \text{ m/s}^2)$

According to the quantum theory,a photon of electromagnetic radiation of frequency $v$ has energy $E = h v$,where $h$ is known as Planck's constant. According to the theory of relativity,a particle of mass $m$ has equivalent energy $E = m c^2$,where $c$ is the speed of light. Thus,a photon can be treated as a particle having effective mass $m = \frac{h v}{c^2}$. If a flash of light is sent horizontally in the Earth's gravitational field,then photons while travelling a horizontal distance $d$ would fall through a vertical distance given by: