In projectile motion, the modulus of rate of change of velocity

There are two points $P$ and $Q$ on a projectile with velocities $v_P$ and $v_Q$ respectively such that $v_P$ is perpendicular to $v_Q$ and $\alpha$ is the angle that $v_P$ makes with horizontal at point $P$. Find the correct option

At $t = 0$ a projectile is fired from a point $O$(taken as origin) on the ground with a speed of $50\,\, m/s$ at an angle of $53^o$ with the horizontal. It just passes two points $A \& B$ each at height $75 \,\,m$ above horizontal as shown. The horizontal separation between the points $A$ and $B$ is …….. $m$

A person can throw a ball upto a maximum range of $100 \,m$. How high above the ground he can throw the same ball?

Define projectile particle and derive the equation $y\, = \,(\tan \,{\theta _0})x\, – \,\frac{g}{{(2\,\cos \,{\theta _0})}}{x^2}$