The equation of a projectile is $y = \sqrt{3}x - \frac{x^2}{2}$. The velocity of projection is:

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:

$A$ person can throw a ball up to a maximum range of $100 \, m$. How high above the ground can he throw the same ball (in $, m$)?

The height of the ceiling in an auditorium is $30 \ m$. $A$ ball is thrown with a speed of $30 \ m \ s^{-1}$ from the entrance such that it just moves very near to the ceiling without touching it and then it reaches the ground at the end of the auditorium. Then the length of the auditorium is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)

Two bullets are fired horizontally and simultaneously towards each other from the rooftops of two buildings $100 \; m$ apart and of the same height of $200 \; m$ with the same velocity of $25 \; m/s$. When and where will the two bullets collide? $(g = 10 \; m/s^2)$

Which of the following remains constant for a projectile fired from the earth?